|\^/| 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 > > adjust_for_pole := proc( > arr_1_pole,h_param > ,arr_1_norms > ,x_start > ,x_end > ,arr_1_y2 > ,arr_1_y1 > ,arr_1_x > ,arr_1_tmp5 > ,arr_1_tmp4 > ,arr_1_tmp3 > ,arr_1_tmp2 > ,arr_1_tmp1 > ,arr_1_tmp0 > ,arr_1_y1_var > ,arr_1_y1_init > ,arr_1_y1_higher > ,arr_1_y1_higher_work > ,arr_1_y1_higher_work2 > ,arr_1_y2_var > ,arr_1_y2_init > ,arr_1_y2_higher > ,arr_1_y2_higher_work > ,arr_1_y2_higher_work2 > ,arr_1_const_0D0 > ,arr_1_const_0 > ,arr_1_const_1 > , arr_1_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local hnew, sz2, tmp; > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(arr_1_y1_higher[1,1]) > glob_small_float) then > tmp := abs(arr_1_y1_higher[1,1]); > if (tmp < glob_normmax) then > glob_normmax := tmp; > fi; > fi;; > if (abs(arr_1_y2_higher[1,1]) > glob_small_float) then > tmp := abs(arr_1_y2_higher[1,1]); > if (tmp < glob_normmax) then > glob_normmax := tmp; > fi; > fi;; > if (glob_look_poles and (abs(arr_1_pole[1]) > glob_small_float) and (arr_1_pole[1] <> glob_large_float)) then > sz2 := arr_1_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); > fi; > fi;; > 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_real_time(); > glob_optimal_start := arr_1_x[1]; > fi;; > hnew := sz2; > #END block > end; adjust_for_pole := proc(arr_1_pole, h_param, arr_1_norms, x_start, x_end, arr_1_y2, arr_1_y1, arr_1_x, arr_1_tmp5, arr_1_tmp4, arr_1_tmp3, arr_1_tmp2, arr_1_tmp1, arr_1_tmp0, arr_1_y1_var, arr_1_y1_init, arr_1_y1_higher, arr_1_y1_higher_work, arr_1_y1_higher_work2, arr_1_y2_var, arr_1_y2_init, arr_1_y2_higher, arr_1_y2_higher_work, arr_1_y2_higher_work2, arr_1_const_0D0, arr_1_const_0, arr_1_const_1, arr_1_m1) local hnew, sz2, tmp; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(arr_1_y1_higher[1, 1]) then tmp := abs(arr_1_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(arr_1_y2_higher[1, 1]) then tmp := abs(arr_1_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(arr_1_pole[1]) and arr_1_pole[1] <> glob_large_float then sz2 := arr_1_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_real_time(); glob_optimal_start := arr_1_x[1] end if; hnew := sz2 end proc > prog_report := proc(iter,opt_iter > ,arr_2_norms > ,x_start > ,x_end > ,arr_2_y2 > ,arr_2_y1 > ,arr_2_x > ,arr_2_tmp5 > ,arr_2_tmp4 > ,arr_2_tmp3 > ,arr_2_tmp2 > ,arr_2_tmp1 > ,arr_2_tmp0 > ,arr_2_y1_var > ,arr_2_y1_init > ,arr_2_y1_higher > ,arr_2_y1_higher_work > ,arr_2_y1_higher_work2 > ,arr_2_y2_var > ,arr_2_y2_init > ,arr_2_y2_higher > ,arr_2_y2_higher_work > ,arr_2_y2_higher_work2 > ,arr_2_const_0D0 > ,arr_2_const_0 > ,arr_2_const_1 > , arr_2_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, optimal_expect_sec, percent_done, total_clock_sec; > > if ((opt_iter mod glob_progress_ind) = 0) then > clock_sec1 := elapsed_real_time(); > total_clock_sec := clock_sec1 - glob_orig_start_sec; > clock_sec := clock_sec1 - glob_clock_start_sec; > left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; > if (glob_reached_optimal_h) then > expect_sec := comp_expect_sec(x_end,x_start,arr_2_x[1] + glob_h , clock_sec1 - glob_orig_start_sec); > opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; > optimal_expect_sec := comp_expect_sec(x_end,x_start,arr_2_x[1] + glob_h , opt_clock_sec); > percent_done := comp_percent(x_end,x_start,arr_2_x[1] + glob_h); > else > expect_sec := 0.0; > optimal_expect_sec := 0.0; > fi;; > omniout_str_noeol(INFO,"Total Elapsed Time = "); > omniout_timestr(total_clock_sec); > omniout_str_noeol(INFO,"Elapsed Time(since restart) = "); > omniout_timestr(clock_sec); > if percent_done < 100.0 then > omniout_str_noeol(INFO,"Expected Time Remaining = "); > omniout_timestr(expect_sec); > omniout_str_noeol(INFO,"Optimized Time Remaining = "); > omniout_timestr(optimal_expect_sec); > fi; > omniout_str_noeol(INFO,"Time to Timeout = "); > omniout_timestr(left_sec); > omniout_float(INFO,"Percent Done ",4,percent_done,4,"%"); > fi;; > end; prog_report := proc(iter, opt_iter, arr_2_norms, x_start, x_end, arr_2_y2, arr_2_y1, arr_2_x, arr_2_tmp5, arr_2_tmp4, arr_2_tmp3, arr_2_tmp2, arr_2_tmp1, arr_2_tmp0, arr_2_y1_var, arr_2_y1_init, arr_2_y1_higher, arr_2_y1_higher_work, arr_2_y1_higher_work2, arr_2_y2_var, arr_2_y2_init, arr_2_y2_higher, arr_2_y2_higher_work, arr_2_y2_higher_work2, arr_2_const_0D0, arr_2_const_0, arr_2_const_1, arr_2_m1) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, optimal_expect_sec, percent_done, total_clock_sec; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; if opt_iter mod glob_progress_ind = 0 then clock_sec1 := elapsed_real_time(); total_clock_sec := clock_sec1 - glob_orig_start_sec; clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; if glob_reached_optimal_h then expect_sec := comp_expect_sec(x_end, x_start, arr_2_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; optimal_expect_sec := comp_expect_sec(x_end, x_start, arr_2_x[1] + glob_h, opt_clock_sec); percent_done := comp_percent(x_end, x_start, arr_2_x[1] + glob_h) else expect_sec := 0.; optimal_expect_sec := 0. end if; omniout_str_noeol(INFO, "Total Elapsed Time = "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) = "); omniout_timestr(clock_sec); if percent_done < 100.0 then omniout_str_noeol(INFO, "Expected Time Remaining = "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining = "); omniout_timestr(optimal_expect_sec) end if; omniout_str_noeol(INFO, "Time to Timeout = "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 4, percent_done, 4, "%") end if end proc > start_all_series := proc(dummy_param > ,arr_3_norms > ,x_start > ,x_end > ,arr_3_y2 > ,arr_3_y1 > ,arr_3_x > ,arr_3_tmp5 > ,arr_3_tmp4 > ,arr_3_tmp3 > ,arr_3_tmp2 > ,arr_3_tmp1 > ,arr_3_tmp0 > ,arr_3_y1_var > ,arr_3_y1_init > ,arr_3_y1_higher > ,arr_3_y1_higher_work > ,arr_3_y1_higher_work2 > ,arr_3_y2_var > ,arr_3_y2_init > ,arr_3_y2_higher > ,arr_3_y2_higher_work > ,arr_3_y2_higher_work2 > ,arr_3_const_0D0 > ,arr_3_const_0 > ,arr_3_const_1 > , arr_3_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local dummy_loc; > start_series( > arr_3_y1,arr_3_y1_higher,arr_3_y1_init,1 > ,arr_3_norms > ,x_start > ,x_end > ,arr_3_const_0D0 > ,arr_3_const_0 > ,arr_3_const_1 > , arr_3_m1 > ); > start_series( > arr_3_y2,arr_3_y2_higher,arr_3_y2_init,1 > ,arr_3_norms > ,x_start > ,x_end > ,arr_3_const_0D0 > ,arr_3_const_0 > ,arr_3_const_1 > , arr_3_m1 > ); > dummy_loc := 1; > end; start_all_series := proc(dummy_param, arr_3_norms, x_start, x_end, arr_3_y2, arr_3_y1, arr_3_x, arr_3_tmp5, arr_3_tmp4, arr_3_tmp3, arr_3_tmp2, arr_3_tmp1, arr_3_tmp0, arr_3_y1_var, arr_3_y1_init, arr_3_y1_higher, arr_3_y1_higher_work, arr_3_y1_higher_work2, arr_3_y2_var, arr_3_y2_init, arr_3_y2_higher, arr_3_y2_higher_work, arr_3_y2_higher_work2, arr_3_const_0D0, arr_3_const_0, arr_3_const_1, arr_3_m1) local dummy_loc; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; start_series(arr_3_y1, arr_3_y1_higher, arr_3_y1_init, 1, arr_3_norms, x_start, x_end, arr_3_const_0D0, arr_3_const_0, arr_3_const_1, arr_3_m1); start_series(arr_3_y2, arr_3_y2_higher, arr_3_y2_init, 1, arr_3_norms, x_start, x_end, arr_3_const_0D0, arr_3_const_0, arr_3_const_1, arr_3_m1); dummy_loc := 1 end proc > jump_all_series := proc(dummy_param > ,arr_4_norms > ,x_start > ,x_end > ,arr_4_y2 > ,arr_4_y1 > ,arr_4_x > ,arr_4_tmp5 > ,arr_4_tmp4 > ,arr_4_tmp3 > ,arr_4_tmp2 > ,arr_4_tmp1 > ,arr_4_tmp0 > ,arr_4_y1_var > ,arr_4_y1_init > ,arr_4_y1_higher > ,arr_4_y1_higher_work > ,arr_4_y1_higher_work2 > ,arr_4_y2_var > ,arr_4_y2_init > ,arr_4_y2_higher > ,arr_4_y2_higher_work > ,arr_4_y2_higher_work2 > ,arr_4_const_0D0 > ,arr_4_const_0 > ,arr_4_const_1 > , arr_4_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local dummy_loc; > jump_series( > arr_4_y1,arr_4_y1_higher,arr_4_y1_higher_work,arr_4_y1_higher_work2,1 > ,arr_4_norms > ,x_start > ,x_end > ,arr_4_const_0D0 > ,arr_4_const_0 > ,arr_4_const_1 > , arr_4_m1 > ); > jump_series( > arr_4_y2,arr_4_y2_higher,arr_4_y2_higher_work,arr_4_y2_higher_work2,1 > ,arr_4_norms > ,x_start > ,x_end > ,arr_4_const_0D0 > ,arr_4_const_0 > ,arr_4_const_1 > , arr_4_m1 > ); > dummy_loc := 1; > end; jump_all_series := proc(dummy_param, arr_4_norms, x_start, x_end, arr_4_y2, arr_4_y1, arr_4_x, arr_4_tmp5, arr_4_tmp4, arr_4_tmp3, arr_4_tmp2, arr_4_tmp1, arr_4_tmp0, arr_4_y1_var, arr_4_y1_init, arr_4_y1_higher, arr_4_y1_higher_work, arr_4_y1_higher_work2, arr_4_y2_var, arr_4_y2_init, arr_4_y2_higher, arr_4_y2_higher_work, arr_4_y2_higher_work2, arr_4_const_0D0, arr_4_const_0, arr_4_const_1, arr_4_m1) local dummy_loc; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; jump_series(arr_4_y1, arr_4_y1_higher, arr_4_y1_higher_work, arr_4_y1_higher_work2, 1, arr_4_norms, x_start, x_end, arr_4_const_0D0, arr_4_const_0, arr_4_const_1, arr_4_m1); jump_series(arr_4_y2, arr_4_y2_higher, arr_4_y2_higher_work, arr_4_y2_higher_work2, 1, arr_4_norms, x_start, x_end, arr_4_const_0D0, arr_4_const_0, arr_4_const_1, arr_4_m1); dummy_loc := 1 end proc > start_series := proc( > arr_5_dep_var_diff,arr_5_dep_var_diff_higher,arr_5_dep_var_diff_init,order_diff > ,arr_5_norms > ,x_start > ,x_end > ,arr_5_const_0D0 > ,arr_5_const_0 > ,arr_5_const_1 > , arr_5_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local r_order, rows, term_no, it; > term_no := 1; > while (term_no <= order_diff) do > arr_5_dep_var_diff[term_no] := evalf( (((arr_5_dep_var_diff_init[term_no])) * glob_h ^ (term_no - 1) / ((factorial_1(term_no - 1))))); > term_no := term_no + 1; > od;; > 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; > arr_5_dep_var_diff_higher[r_order,term_no] := evalf( (((arr_5_dep_var_diff_init[it])) * (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))))); > term_no := term_no + 1; > od;; > r_order := r_order + 1; > od;; > end; start_series := proc(arr_5_dep_var_diff, arr_5_dep_var_diff_higher, arr_5_dep_var_diff_init, order_diff, arr_5_norms, x_start, x_end, arr_5_const_0D0, arr_5_const_0, arr_5_const_1, arr_5_m1) local r_order, rows, term_no, it; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; term_no := 1; while term_no <= order_diff do arr_5_dep_var_diff[term_no] := evalf( arr_5_dep_var_diff_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; arr_5_dep_var_diff_higher[r_order, term_no] := evalf( arr_5_dep_var_diff_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 end proc > jump_series := proc( > arr_6_dep_var_diff,arr_6_dep_var_diff_higher,arr_6_dep_var_diff_higher_work, arr_6_dep_var_diff_higher_work2, order_diff > ,arr_6_norms > ,x_start > ,x_end > ,arr_6_const_0D0 > ,arr_6_const_0 > ,arr_6_const_1 > , arr_6_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local ord, term_no; #START PART 1 SUM AND ADJUST) > sum_and_adjust(arr_6_dep_var_diff_higher,arr_6_dep_var_diff_higher_work, arr_6_dep_var_diff_higher_work2,order_diff); #END PART 1 #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do > arr_6_dep_var_diff[term_no] := arr_6_dep_var_diff_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do > arr_6_dep_var_diff_higher[ord,term_no] := arr_6_dep_var_diff_higher_work2[ord,term_no]; > ord := ord + 1; > od;; > term_no := term_no - 1; > od;; #END PART 2 HEVE MOVED TERMS to REGULAR Array > end; jump_series := proc(arr_6_dep_var_diff, arr_6_dep_var_diff_higher, arr_6_dep_var_diff_higher_work, arr_6_dep_var_diff_higher_work2, order_diff, arr_6_norms, x_start, x_end, arr_6_const_0D0, arr_6_const_0, arr_6_const_1, arr_6_m1) local ord, term_no; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; sum_and_adjust(arr_6_dep_var_diff_higher, arr_6_dep_var_diff_higher_work, arr_6_dep_var_diff_higher_work2, order_diff); term_no := glob_max_terms; while 1 <= term_no do arr_6_dep_var_diff[term_no] := arr_6_dep_var_diff_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do arr_6_dep_var_diff_higher[ord, term_no] := arr_6_dep_var_diff_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end proc > check_for_pole := proc( > arr_7_pole > ,arr_7_norms > ,x_start > ,x_end > ,arr_7_y2 > ,arr_7_y1 > ,arr_7_x > ,arr_7_tmp5 > ,arr_7_tmp4 > ,arr_7_tmp3 > ,arr_7_tmp2 > ,arr_7_tmp1 > ,arr_7_tmp0 > ,arr_7_y1_var > ,arr_7_y1_init > ,arr_7_y1_higher > ,arr_7_y1_higher_work > ,arr_7_y1_higher_work2 > ,arr_7_y2_var > ,arr_7_y2_init > ,arr_7_y2_higher > ,arr_7_y2_higher_work > ,arr_7_y2_higher_work2 > ,arr_7_const_0D0 > ,arr_7_const_0 > ,arr_7_const_1 > , arr_7_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local arr_7_ans_complex,arr_7_ans_real,arr_7_old_pole; > arr_7_ans_real := Array(1..(2 + 1),[]); > arr_7_ans_complex := Array(1..(2 + 1),[]); > arr_7_old_pole := Array(1..(2 + 1),[]); > arr_7_old_pole[1] := glob_large_float; > arr_7_old_pole[2] := glob_large_float; > arr_7_old_pole[3] := glob_large_float; > arr_7_ans_real[1] := glob_large_float; > arr_7_ans_real[2] := glob_large_float; > arr_7_ans_real[3] := glob_large_float; > arr_7_ans_complex[1] := glob_large_float; > arr_7_ans_complex[2] := glob_large_float; > arr_7_ans_complex[3] := glob_large_float; > radius_real(arr_7_y1_higher,1, arr_7_ans_real); > radius_complex(arr_7_y1_higher,1, arr_7_ans_complex); > which_radius(arr_7_pole,arr_7_ans_real,arr_7_ans_complex); > if (arr_7_pole[1] < arr_7_old_pole[1]) then > arr_7_old_pole[1] := arr_7_pole[1]; > arr_7_old_pole[2] := arr_7_pole[2]; > fi;; > radius_real(arr_7_y2_higher,1, arr_7_ans_real); > radius_complex(arr_7_y2_higher,1, arr_7_ans_complex); > which_radius(arr_7_pole,arr_7_ans_real,arr_7_ans_complex); > if (arr_7_pole[1] < arr_7_old_pole[1]) then > arr_7_old_pole[1] := arr_7_pole[1]; > arr_7_old_pole[2] := arr_7_pole[2]; > fi;; > arr_7_pole[1] := arr_7_old_pole[1]; > arr_7_pole[2] := arr_7_old_pole[2]; > end; check_for_pole := proc(arr_7_pole, arr_7_norms, x_start, x_end, arr_7_y2, arr_7_y1, arr_7_x, arr_7_tmp5, arr_7_tmp4, arr_7_tmp3, arr_7_tmp2, arr_7_tmp1, arr_7_tmp0, arr_7_y1_var, arr_7_y1_init, arr_7_y1_higher, arr_7_y1_higher_work, arr_7_y1_higher_work2, arr_7_y2_var, arr_7_y2_init, arr_7_y2_higher, arr_7_y2_higher_work, arr_7_y2_higher_work2, arr_7_const_0D0, arr_7_const_0, arr_7_const_1, arr_7_m1) local arr_7_ans_complex, arr_7_ans_real, arr_7_old_pole; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; arr_7_ans_real := Array(1 .. 3, []); arr_7_ans_complex := Array(1 .. 3, []); arr_7_old_pole := Array(1 .. 3, []); arr_7_old_pole[1] := glob_large_float; arr_7_old_pole[2] := glob_large_float; arr_7_old_pole[3] := glob_large_float; arr_7_ans_real[1] := glob_large_float; arr_7_ans_real[2] := glob_large_float; arr_7_ans_real[3] := glob_large_float; arr_7_ans_complex[1] := glob_large_float; arr_7_ans_complex[2] := glob_large_float; arr_7_ans_complex[3] := glob_large_float; radius_real(arr_7_y1_higher, 1, arr_7_ans_real); radius_complex(arr_7_y1_higher, 1, arr_7_ans_complex); which_radius(arr_7_pole, arr_7_ans_real, arr_7_ans_complex); if arr_7_pole[1] < arr_7_old_pole[1] then arr_7_old_pole[1] := arr_7_pole[1]; arr_7_old_pole[2] := arr_7_pole[2] end if; radius_real(arr_7_y2_higher, 1, arr_7_ans_real); radius_complex(arr_7_y2_higher, 1, arr_7_ans_complex); which_radius(arr_7_pole, arr_7_ans_real, arr_7_ans_complex); if arr_7_pole[1] < arr_7_old_pole[1] then arr_7_old_pole[1] := arr_7_pole[1]; arr_7_old_pole[2] := arr_7_pole[2] end if; arr_7_pole[1] := arr_7_old_pole[1]; arr_7_pole[2] := arr_7_old_pole[2] end proc > display_alot := proc(iter > ,arr_8_norms > ,x_start > ,x_end > ,arr_8_y2 > ,arr_8_y1 > ,arr_8_x > ,arr_8_tmp5 > ,arr_8_tmp4 > ,arr_8_tmp3 > ,arr_8_tmp2 > ,arr_8_tmp1 > ,arr_8_tmp0 > ,arr_8_y1_var > ,arr_8_y1_init > ,arr_8_y1_higher > ,arr_8_y1_higher_work > ,arr_8_y1_higher_work2 > ,arr_8_y2_var > ,arr_8_y2_init > ,arr_8_y2_higher > ,arr_8_y2_higher_work > ,arr_8_y2_higher_work2 > ,arr_8_const_0D0 > ,arr_8_const_0 > ,arr_8_const_1 > , arr_8_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local abserr, analytic_val_y,dummy, ind_var, numeric_val, relerr, term_no; > if (iter >= 0) then > ind_var := evalf(arr_8_x[1]); > omniout_float(ALWAYS,"x[1] = ",20,ind_var,20,""); > analytic_val_y := evalf(exact_soln_y1(ind_var)); > omniout_float(ALWAYS,"y1(analytic)=",32,analytic_val_y,20,""); > term_no := 1; > numeric_val := evalf(arr_8_y1[term_no]); > abserr := evalf(abs(numeric_val - analytic_val_y)); > omniout_float(ALWAYS,"y1(numeric) =",32, numeric_val, 20,""); > if (abs(analytic_val_y) <> 0.0) then > relerr := evalf(abserr*100.0/abs(analytic_val_y)); > else > relerr := -1.0 ; > fi;; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"glob_h ",20,glob_h,20," ") > ; > analytic_val_y := evalf(exact_soln_y2(ind_var)); > omniout_float(ALWAYS,"y2(analytic)=",32,analytic_val_y,20,""); > term_no := 1; > numeric_val := evalf(arr_8_y2[term_no]); > abserr := evalf(abs(numeric_val - analytic_val_y)); > omniout_float(ALWAYS,"y2(numeric) =",32, numeric_val, 20,""); > if (abs(analytic_val_y) <> 0.0) then > relerr := evalf(abserr*100.0/abs(analytic_val_y)); > else > relerr := -1.0 ; > fi;; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"glob_h ",20,glob_h,20," ") > fi;; > dummy := 1; > end; display_alot := proc(iter, arr_8_norms, x_start, x_end, arr_8_y2, arr_8_y1, arr_8_x, arr_8_tmp5, arr_8_tmp4, arr_8_tmp3, arr_8_tmp2, arr_8_tmp1, arr_8_tmp0, arr_8_y1_var, arr_8_y1_init, arr_8_y1_higher, arr_8_y1_higher_work, arr_8_y1_higher_work2, arr_8_y2_var, arr_8_y2_init, arr_8_y2_higher, arr_8_y2_higher_work, arr_8_y2_higher_work2, arr_8_const_0D0, arr_8_const_0, arr_8_const_1, arr_8_m1) local abserr, analytic_val_y, dummy, ind_var, numeric_val, relerr, term_no; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; if 0 <= iter then ind_var := evalf(arr_8_x[1]); omniout_float(ALWAYS, "x[1] = ", 20, ind_var, 20, ""); analytic_val_y := evalf(exact_soln_y1(ind_var)); omniout_float(ALWAYS, "y1(analytic)=", 32, analytic_val_y, 20, ""); term_no := 1; numeric_val := evalf(arr_8_y1[term_no]); abserr := evalf(abs(numeric_val - analytic_val_y)); omniout_float(ALWAYS, "y1(numeric) =", 32, numeric_val, 20, ""); if abs(analytic_val_y) <> 0. then relerr := evalf(abserr*100.0/abs(analytic_val_y)) else relerr := -1.0 end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "glob_h ", 20, glob_h, 20, " "); analytic_val_y := evalf(exact_soln_y2(ind_var)); omniout_float(ALWAYS, "y2(analytic)=", 32, analytic_val_y, 20, ""); term_no := 1; numeric_val := evalf(arr_8_y2[term_no]); abserr := evalf(abs(numeric_val - analytic_val_y)); omniout_float(ALWAYS, "y2(numeric) =", 32, numeric_val, 20, ""); if abs(analytic_val_y) <> 0. then relerr := evalf(abserr*100.0/abs(analytic_val_y)) else relerr := -1.0 end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "glob_h ", 20, glob_h, 20, " ") end if; dummy := 1 end proc > get_norms := proc( > dummy_param > ,arr_9_norms > ,x_start > ,x_end > ,arr_9_y2 > ,arr_9_y1 > ,arr_9_x > ,arr_9_tmp5 > ,arr_9_tmp4 > ,arr_9_tmp3 > ,arr_9_tmp2 > ,arr_9_tmp1 > ,arr_9_tmp0 > ,arr_9_y1_var > ,arr_9_y1_init > ,arr_9_y1_higher > ,arr_9_y1_higher_work > ,arr_9_y1_higher_work2 > ,arr_9_y2_var > ,arr_9_y2_init > ,arr_9_y2_higher > ,arr_9_y2_higher_work > ,arr_9_y2_higher_work2 > ,arr_9_const_0D0 > ,arr_9_const_0 > ,arr_9_const_1 > , arr_9_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local iii; > if (not glob_initial_pass) then > set_z(arr_9_norms,glob_max_terms+1); > iii := 1; > while (iii <= glob_max_terms) do > if (abs(arr_9_y1[iii]) > arr_9_norms[iii]) then > arr_9_norms[iii] := abs(arr_9_y1[iii]); > fi;; > iii := iii + 1; > od; > ; > iii := 1; > while (iii <= glob_max_terms) do > if (abs(arr_9_y2[iii]) > arr_9_norms[iii]) then > arr_9_norms[iii] := abs(arr_9_y2[iii]); > fi;; > iii := iii + 1; > od; > ; > fi;; > end; get_norms := proc(dummy_param, arr_9_norms, x_start, x_end, arr_9_y2, arr_9_y1, arr_9_x, arr_9_tmp5, arr_9_tmp4, arr_9_tmp3, arr_9_tmp2, arr_9_tmp1, arr_9_tmp0, arr_9_y1_var, arr_9_y1_init, arr_9_y1_higher, arr_9_y1_higher_work, arr_9_y1_higher_work2, arr_9_y2_var, arr_9_y2_init, arr_9_y2_higher, arr_9_y2_higher_work, arr_9_y2_higher_work2, arr_9_const_0D0, arr_9_const_0, arr_9_const_1, arr_9_m1) local iii; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; if not glob_initial_pass then set_z(arr_9_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if arr_9_norms[iii] < abs(arr_9_y1[iii]) then arr_9_norms[iii] := abs(arr_9_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if arr_9_norms[iii] < abs(arr_9_y2[iii]) then arr_9_norms[iii] := abs(arr_9_y2[iii]) end if; iii := iii + 1 end do end if end proc > atomall := proc(dummy_param > ,arr_10_norms > ,x_start > ,x_end > ,arr_10_y2 > ,arr_10_y1 > ,arr_10_x > ,arr_10_tmp5 > ,arr_10_tmp4 > ,arr_10_tmp3 > ,arr_10_tmp2 > ,arr_10_tmp1 > ,arr_10_tmp0 > ,arr_10_y1_var > ,arr_10_y1_init > ,arr_10_y1_higher > ,arr_10_y1_higher_work > ,arr_10_y1_higher_work2 > ,arr_10_y2_var > ,arr_10_y2_init > ,arr_10_y2_higher > ,arr_10_y2_higher_work > ,arr_10_y2_higher_work2 > ,arr_10_const_0D0 > ,arr_10_const_0 > ,arr_10_const_1 > , arr_10_m1 > ) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > > local kkk, order_d, dummy,adj2,temporary,term; #END OUTFILE1 #BEGIN ATOMHDR1 #emit pre diff $eq_no = 1 i = 1 > arr_10_tmp1[1] := arr_10_y2_higher[1,1]; # emit pre mult $eq_no = 1 i = 1 > arr_10_tmp2[1] := (arr_10_m1[1] * (arr_10_tmp1[1])); #emit pre add $eq_no = 1 i = 1 > arr_10_tmp3[1] := evalf(arr_10_const_0D0[1] + arr_10_tmp2[1]); #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then > temporary := arr_10_tmp3[1] * (glob_h ^ (1)) * factorial_3(0,1); > arr_10_y1[2] := temporary; > arr_10_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y1_higher[2,1] := temporary; > ; > fi; > kkk := 2; #emit pre diff $eq_no = 2 i = 1 > arr_10_tmp5[1] := arr_10_y1_higher[1,1]; #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then > temporary := arr_10_tmp5[1] * (glob_h ^ (1)) * factorial_3(0,1); > arr_10_y2[2] := temporary; > arr_10_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y2_higher[2,1] := temporary; > ; > fi; > kkk := 2; #END ATOMHDR1 #BEGIN ATOMHDR2 #emit pre diff $eq_no = 1 i = 2 > arr_10_tmp1[2] := arr_10_y2_higher[1,2]; # emit pre mult $eq_no = 1 i = 2 > arr_10_tmp2[2] := ats(2,arr_10_m1,arr_10_tmp1,1); #emit pre add $eq_no = 1 i = 2 > arr_10_tmp3[2] := evalf(arr_10_const_0D0[2] + arr_10_tmp2[2]); #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then > temporary := arr_10_tmp3[2] * (glob_h ^ (1)) * factorial_3(1,2); > arr_10_y1[3] := temporary; > arr_10_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y1_higher[2,2] := temporary; > ; > fi; > kkk := 3; #emit pre diff $eq_no = 2 i = 2 > arr_10_tmp5[2] := arr_10_y1_higher[1,2]; #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then > temporary := arr_10_tmp5[2] * (glob_h ^ (1)) * factorial_3(1,2); > arr_10_y2[3] := temporary; > arr_10_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y2_higher[2,2] := temporary; > ; > fi; > kkk := 3; #END ATOMHDR2 #BEGIN ATOMHDR3 #emit pre diff $eq_no = 1 i = 3 > arr_10_tmp1[3] := arr_10_y2_higher[1,3]; # emit pre mult $eq_no = 1 i = 3 > arr_10_tmp2[3] := ats(3,arr_10_m1,arr_10_tmp1,1); #emit pre add $eq_no = 1 i = 3 > arr_10_tmp3[3] := evalf(arr_10_const_0D0[3] + arr_10_tmp2[3]); #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then > temporary := arr_10_tmp3[3] * (glob_h ^ (1)) * factorial_3(2,3); > arr_10_y1[4] := temporary; > arr_10_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y1_higher[2,3] := temporary; > ; > fi; > kkk := 4; #emit pre diff $eq_no = 2 i = 3 > arr_10_tmp5[3] := arr_10_y1_higher[1,3]; #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then > temporary := arr_10_tmp5[3] * (glob_h ^ (1)) * factorial_3(2,3); > arr_10_y2[4] := temporary; > arr_10_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y2_higher[2,3] := temporary; > ; > fi; > kkk := 4; #END ATOMHDR3 #BEGIN ATOMHDR4 #emit pre diff $eq_no = 1 i = 4 > arr_10_tmp1[4] := arr_10_y2_higher[1,4]; # emit pre mult $eq_no = 1 i = 4 > arr_10_tmp2[4] := ats(4,arr_10_m1,arr_10_tmp1,1); #emit pre add $eq_no = 1 i = 4 > arr_10_tmp3[4] := evalf(arr_10_const_0D0[4] + arr_10_tmp2[4]); #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then > temporary := arr_10_tmp3[4] * (glob_h ^ (1)) * factorial_3(3,4); > arr_10_y1[5] := temporary; > arr_10_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y1_higher[2,4] := temporary; > ; > fi; > kkk := 5; #emit pre diff $eq_no = 2 i = 4 > arr_10_tmp5[4] := arr_10_y1_higher[1,4]; #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then > temporary := arr_10_tmp5[4] * (glob_h ^ (1)) * factorial_3(3,4); > arr_10_y2[5] := temporary; > arr_10_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y2_higher[2,4] := temporary; > ; > fi; > kkk := 5; #END ATOMHDR4 #BEGIN ATOMHDR5 #emit pre diff $eq_no = 1 i = 5 > arr_10_tmp1[5] := arr_10_y2_higher[1,5]; # emit pre mult $eq_no = 1 i = 5 > arr_10_tmp2[5] := ats(5,arr_10_m1,arr_10_tmp1,1); #emit pre add $eq_no = 1 i = 5 > arr_10_tmp3[5] := evalf(arr_10_const_0D0[5] + arr_10_tmp2[5]); #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then > temporary := arr_10_tmp3[5] * (glob_h ^ (1)) * factorial_3(4,5); > arr_10_y1[6] := temporary; > arr_10_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y1_higher[2,5] := temporary; > ; > fi; > kkk := 6; #emit pre diff $eq_no = 2 i = 5 > arr_10_tmp5[5] := arr_10_y1_higher[1,5]; #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then > temporary := arr_10_tmp5[5] * (glob_h ^ (1)) * factorial_3(4,5); > arr_10_y2[6] := temporary; > arr_10_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2); > arr_10_y2_higher[2,5] := temporary; > ; > fi; > kkk := 6; #END ATOMHDR5 #BEGIN OUTFILE3 > while (kkk <= glob_max_terms) do #END OUTFILE3 #BEGIN OUTFILE4 #emit diff $eq_no = 1 > arr_10_tmp1[kkk] := arr_10_y2_higher[1,kkk]; #emit mult $eq_no = 1 > arr_10_tmp2[kkk] := ats(kkk,arr_10_m1,arr_10_tmp1,1); #emit add $eq_no = 1 > arr_10_tmp3[kkk] := evalf(arr_10_const_0D0[kkk] + arr_10_tmp2[kkk]); #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then > temporary := arr_10_tmp3[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > arr_10_y1[kkk + order_d] := temporary; > arr_10_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do > temporary := temporary / glob_h * adj2; > arr_10_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od; > fi;; #emit diff $eq_no = 2 > arr_10_tmp5[kkk] := arr_10_y1_higher[1,kkk]; #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then > temporary := arr_10_tmp5[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > arr_10_y2[kkk + order_d] := temporary; > arr_10_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do > temporary := temporary / glob_h * adj2; > arr_10_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od; > fi;; > kkk := kkk + 1; > od;; > dummy := 1; #END OUTFILE4 #BEGIN OUTFILE5 > end; atomall := proc(dummy_param, arr_10_norms, x_start, x_end, arr_10_y2, arr_10_y1, arr_10_x, arr_10_tmp5, arr_10_tmp4, arr_10_tmp3, arr_10_tmp2, arr_10_tmp1, arr_10_tmp0, arr_10_y1_var, arr_10_y1_init, arr_10_y1_higher, arr_10_y1_higher_work, arr_10_y1_higher_work2, arr_10_y2_var, arr_10_y2_init, arr_10_y2_higher, arr_10_y2_higher_work, arr_10_y2_higher_work2, arr_10_const_0D0, arr_10_const_0, arr_10_const_1, arr_10_m1) local kkk, order_d, dummy, adj2, temporary, term; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; arr_10_tmp1[1] := arr_10_y2_higher[1, 1]; arr_10_tmp2[1] := arr_10_m1[1]*arr_10_tmp1[1]; arr_10_tmp3[1] := evalf(arr_10_const_0D0[1] + arr_10_tmp2[1]); if 1 <= glob_max_terms then temporary := arr_10_tmp3[1]*glob_h*factorial_3(0, 1); arr_10_y1[2] := temporary; arr_10_y1_higher[1, 2] := temporary; temporary := 2*temporary/glob_h; arr_10_y1_higher[2, 1] := temporary end if; kkk := 2; arr_10_tmp5[1] := arr_10_y1_higher[1, 1]; if 1 <= glob_max_terms then temporary := arr_10_tmp5[1]*glob_h*factorial_3(0, 1); arr_10_y2[2] := temporary; arr_10_y2_higher[1, 2] := temporary; temporary := 2*temporary/glob_h; arr_10_y2_higher[2, 1] := temporary end if; kkk := 2; arr_10_tmp1[2] := arr_10_y2_higher[1, 2]; arr_10_tmp2[2] := ats(2, arr_10_m1, arr_10_tmp1, 1); arr_10_tmp3[2] := evalf(arr_10_const_0D0[2] + arr_10_tmp2[2]); if 2 <= glob_max_terms then temporary := arr_10_tmp3[2]*glob_h*factorial_3(1, 2); arr_10_y1[3] := temporary; arr_10_y1_higher[1, 3] := temporary; temporary := 2*temporary/glob_h; arr_10_y1_higher[2, 2] := temporary end if; kkk := 3; arr_10_tmp5[2] := arr_10_y1_higher[1, 2]; if 2 <= glob_max_terms then temporary := arr_10_tmp5[2]*glob_h*factorial_3(1, 2); arr_10_y2[3] := temporary; arr_10_y2_higher[1, 3] := temporary; temporary := 2*temporary/glob_h; arr_10_y2_higher[2, 2] := temporary end if; kkk := 3; arr_10_tmp1[3] := arr_10_y2_higher[1, 3]; arr_10_tmp2[3] := ats(3, arr_10_m1, arr_10_tmp1, 1); arr_10_tmp3[3] := evalf(arr_10_const_0D0[3] + arr_10_tmp2[3]); if 3 <= glob_max_terms then temporary := arr_10_tmp3[3]*glob_h*factorial_3(2, 3); arr_10_y1[4] := temporary; arr_10_y1_higher[1, 4] := temporary; temporary := 2*temporary/glob_h; arr_10_y1_higher[2, 3] := temporary end if; kkk := 4; arr_10_tmp5[3] := arr_10_y1_higher[1, 3]; if 3 <= glob_max_terms then temporary := arr_10_tmp5[3]*glob_h*factorial_3(2, 3); arr_10_y2[4] := temporary; arr_10_y2_higher[1, 4] := temporary; temporary := 2*temporary/glob_h; arr_10_y2_higher[2, 3] := temporary end if; kkk := 4; arr_10_tmp1[4] := arr_10_y2_higher[1, 4]; arr_10_tmp2[4] := ats(4, arr_10_m1, arr_10_tmp1, 1); arr_10_tmp3[4] := evalf(arr_10_const_0D0[4] + arr_10_tmp2[4]); if 4 <= glob_max_terms then temporary := arr_10_tmp3[4]*glob_h*factorial_3(3, 4); arr_10_y1[5] := temporary; arr_10_y1_higher[1, 5] := temporary; temporary := 2*temporary/glob_h; arr_10_y1_higher[2, 4] := temporary end if; kkk := 5; arr_10_tmp5[4] := arr_10_y1_higher[1, 4]; if 4 <= glob_max_terms then temporary := arr_10_tmp5[4]*glob_h*factorial_3(3, 4); arr_10_y2[5] := temporary; arr_10_y2_higher[1, 5] := temporary; temporary := 2*temporary/glob_h; arr_10_y2_higher[2, 4] := temporary end if; kkk := 5; arr_10_tmp1[5] := arr_10_y2_higher[1, 5]; arr_10_tmp2[5] := ats(5, arr_10_m1, arr_10_tmp1, 1); arr_10_tmp3[5] := evalf(arr_10_const_0D0[5] + arr_10_tmp2[5]); if 5 <= glob_max_terms then temporary := arr_10_tmp3[5]*glob_h*factorial_3(4, 5); arr_10_y1[6] := temporary; arr_10_y1_higher[1, 6] := temporary; temporary := 2*temporary/glob_h; arr_10_y1_higher[2, 5] := temporary end if; kkk := 6; arr_10_tmp5[5] := arr_10_y1_higher[1, 5]; if 5 <= glob_max_terms then temporary := arr_10_tmp5[5]*glob_h*factorial_3(4, 5); arr_10_y2[6] := temporary; arr_10_y2_higher[1, 6] := temporary; temporary := 2*temporary/glob_h; arr_10_y2_higher[2, 5] := temporary end if; kkk := 6; while kkk <= glob_max_terms do arr_10_tmp1[kkk] := arr_10_y2_higher[1, kkk]; arr_10_tmp2[kkk] := ats(kkk, arr_10_m1, arr_10_tmp1, 1); arr_10_tmp3[kkk] := evalf(arr_10_const_0D0[kkk] + arr_10_tmp2[kkk]) ; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := arr_10_tmp3[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); arr_10_y1[kkk + order_d] := temporary; arr_10_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*adj2/glob_h; arr_10_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; arr_10_tmp5[kkk] := arr_10_y1_higher[1, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := arr_10_tmp5[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); arr_10_y2[kkk + order_d] := temporary; arr_10_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*adj2/glob_h; arr_10_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; kkk := kkk + 1 end do; dummy := 1 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; 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; 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; 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; 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; 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; 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, > arr_11_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,arr_11_series[i]); > i := i + 1; > od; > fi; > end; dump_series := proc(iolevel, dump_label, series_name, arr_11_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_11_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > arr_12_series2,numb,subnum,arr_12_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,arr_12_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_12_series2, numb, subnum, arr_12_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, arr_12_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; 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 > 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 := ev(secs_in,float); > if (secs > 0.0) then > sec_in_millinium := ev(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium,float); > milliniums := ev((secs / sec_in_millinium),float); > 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 > 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 > 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 > 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 > printf("%d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then > printf("%d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then > printf("%d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf("%d Seconds\n",sec_int); > fi; > else > printf(" Unknown\n"); > fi; > 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 := ev(secs_in, float); if 0. < secs then sec_in_millinium := ev(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium, float); milliniums := ev(secs/sec_in_millinium, float); 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 Ye\ ars %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 > > set_z := proc( > arr_14_a,t) > local iii; > iii := 1; > while (iii <= t) do > arr_14_a[iii] := 0.0; > iii := iii + 1; > od; > end; set_z := proc(arr_14_a, t) local iii; iii := 1; while iii <= t do arr_14_a[iii] := 0.; iii := iii + 1 end do end proc > set_zz := proc( > arr_15_a,t,mx_ord) > local iii,jjj; > iii := 1; > while (iii <= mx_ord) do > jjj := 1; > while (jjj <= t) do > arr_15_a[iii,jjj] := 0.0; > jjj := jjj + 1; > od;; > iii := iii + 1; > od; > end; set_zz := proc(arr_15_a, t, mx_ord) local iii, jjj; iii := 1; while iii <= mx_ord do jjj := 1; while jjj <= t do arr_15_a[iii, jjj] := 0.; jjj := jjj + 1 end do; iii := iii + 1 end do end proc > set_z2 := proc( > arr_16_a,start) > global glob_max_terms; > local iii; > iii := start; > while (iii <= (glob_max_terms)) do > arr_16_a[i] := 0.0; > iii := iii + 1; > od; > end; set_z2 := proc(arr_16_a, start) local iii; global glob_max_terms; iii := start; while iii <= glob_max_terms do arr_16_a[i] := 0.; iii := iii + 1 end do end proc > set_zz2 := proc( > arr_17_a,mx_ord,start) > global glob_max_terms; > local iii,jjj; > iii := 1; > while (iii <= (mx_ord)) do > jjj := start; > while (jjj <= (glob_max_terms)) do > arr_17_a[iii] := 0.0; > jjj := jjj + 1; > od;; > iii := iii + 1; > od; > end; set_zz2 := proc(arr_17_a, mx_ord, start) local iii, jjj; global glob_max_terms; iii := 1; while iii <= mx_ord do jjj := start; while jjj <= glob_max_terms do arr_17_a[iii] := 0.; jjj := jjj + 1 end do; iii := iii + 1 end do end proc > > ats := proc( > mmm_ats,arr_18_a,arr_18_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > 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 + arr_18_a[iii_ats]*arr_18_b[lll_ats]; > iii_ats := iii_ats + 1; > od; > fi;; > ret_ats > end; ats := proc(mmm_ats, arr_18_a, arr_18_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 + arr_18_a[iii_ats]*arr_18_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > att := proc( > mmm_att,arr_19_aa,arr_19_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 > 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 + arr_19_aa[iii_att]*arr_19_bb[lll_att]*ev(al_att,float); > fi;; > iii_att := iii_att + 1; > od;; > ret_att := ret_att / ev(mmm_att,float) ; > fi;; > ret_att; > end; att := proc(mmm_att, arr_19_aa, arr_19_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 + arr_19_aa[iii_att]*arr_19_bb[lll_att]*ev(al_att, float) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/ev(mmm_att, float) end if; ret_att end proc > > radius_real := proc( > arr_20_y_higher,order_diff,arr_20_ans) > global glob_h,glob_large_float, glob_max_terms, glob_small_float; > local hdrc, m, n, ord_no, rcs, rm0, rm1; #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. #Applies to pole of arbitrary r_order on the real axis, #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - order_diff - 1; > while ((m > 3) and ((abs(arr_20_y_higher[1,m]) < glob_small_float) or (abs(arr_20_y_higher[1,m-1]) < glob_small_float) or (abs(arr_20_y_higher[1,m-2]) < glob_small_float ))) do > m := m - 1; > od;; > if (m > 3) then > rm0 := evalf( arr_20_y_higher[1,m]/arr_20_y_higher[1,m-1]); > rm1 := evalf( arr_20_y_higher[1,m-1]/arr_20_y_higher[1,m-2]); > hdrc := evalf(ev(m-1,float)*rm0-ev(m-2,float)*rm1); > if (abs(hdrc) > glob_small_float) then > rcs := evalf( glob_h/hdrc); > ord_no := evalf( ev(m-1,float)*rm0/hdrc - ev(m,float) + 2.0); > arr_20_ans[1] := rcs; > arr_20_ans[2] := ord_no; > else > arr_20_ans[1] := glob_large_float; > arr_20_ans[2] := glob_large_float; > fi; > else > arr_20_ans[1] := glob_large_float; > arr_20_ans[2] := glob_large_float; > fi; > end; radius_real := proc(arr_20_y_higher, order_diff, arr_20_ans) local hdrc, m, n, ord_no, rcs, rm0, rm1; global glob_h, glob_large_float, glob_max_terms, glob_small_float; n := glob_max_terms; m := n - order_diff - 1; while 3 < m and (abs(arr_20_y_higher[1, m]) < glob_small_float or abs(arr_20_y_higher[1, m - 1]) < glob_small_float or abs(arr_20_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 3 < m then rm0 := evalf(arr_20_y_higher[1, m]/arr_20_y_higher[1, m - 1]); rm1 := evalf(arr_20_y_higher[1, m - 1]/arr_20_y_higher[1, m - 2]); hdrc := evalf(ev(m - 1, float)*rm0 - ev(m - 2, float)*rm1); if glob_small_float < abs(hdrc) then rcs := evalf(glob_h/hdrc); ord_no := evalf(ev(m - 1, float)*rm0/hdrc - ev(m, float) + 2.0) ; arr_20_ans[1] := rcs; arr_20_ans[2] := ord_no else arr_20_ans[1] := glob_large_float; arr_20_ans[2] := glob_large_float end if else arr_20_ans[1] := glob_large_float; arr_20_ans[2] := glob_large_float end if end proc > radius_complex := proc( > arr_21_y_higher,order_diff,arr_21_ans) > global glob_h,glob_large_float, glob_max_terms, glob_small_float; > local cnt, dr1, dr2, ds1, ds2, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4; > #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; > cnt := 0; > while ((cnt < 5) and (n >= 1)) do > if (abs(arr_21_y_higher[1,n]) > glob_small_float) then > cnt := cnt + 1; > else > cnt := 0; > fi;; > n := n - 1; > od;; > m := n + cnt; > if (m < 6) then > arr_21_ans[1] := glob_large_float; > arr_21_ans[2] := glob_large_float; > return(); > fi;; > if (abs(arr_21_y_higher[1,m]) >= (glob_large_float)) or (abs(arr_21_y_higher[1,m-1]) >=(glob_large_float)) or (abs(arr_21_y_higher[1,m-2]) >= (glob_large_float)) or (abs(arr_21_y_higher[1,m-3]) >= (glob_large_float)) or (abs(arr_21_y_higher[1,m-4]) >= (glob_large_float)) or (abs(arr_21_y_higher[1,m-5]) >= (glob_large_float)) then > arr_21_ans[1] := glob_large_float; > arr_21_ans[2] := glob_large_float; > return(); > else > rm0 := (arr_21_y_higher[1,m])/(arr_21_y_higher[1,m-1]); > rm1 := (arr_21_y_higher[1,m-1])/(arr_21_y_higher[1,m-2]); > rm2 := (arr_21_y_higher[1,m-2])/(arr_21_y_higher[1,m-3]); > rm3 := (arr_21_y_higher[1,m-3])/(arr_21_y_higher[1,m-4]); > rm4 := (arr_21_y_higher[1,m-4])/(arr_21_y_higher[1,m-5]); > nr1 := ev(m-1,float)*rm0 - 2.0*ev(m-2,float)*rm1 + ev(m-3,float)*rm2; > nr2 := ev(m-2,float)*rm1 - 2.0*ev(m-3,float)*rm2 + ev(m-4,float)*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 > arr_21_ans[1] := (glob_large_float); > arr_21_ans[2] := (glob_large_float); > return(); > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then > 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) -(m)/2.0; > if (abs(rcs) > glob_small_float) then > if (rcs > 0.0) then > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi; > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi; > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi; > fi;; > arr_21_ans[1] := rad_c; > arr_21_ans[2] := ord_no; > return(); > fi; > > end; radius_complex := proc(arr_21_y_higher, order_diff, arr_21_ans) local cnt, dr1, dr2, ds1, ds2, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4; global glob_h, glob_large_float, glob_max_terms, glob_small_float; n := glob_max_terms; cnt := 0; while cnt < 5 and 1 <= n do if glob_small_float < abs(arr_21_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m < 6 then arr_21_ans[1] := glob_large_float; arr_21_ans[2] := glob_large_float; return end if; if glob_large_float <= abs(arr_21_y_higher[1, m]) or glob_large_float <= abs(arr_21_y_higher[1, m - 1]) or glob_large_float <= abs(arr_21_y_higher[1, m - 2]) or glob_large_float <= abs(arr_21_y_higher[1, m - 3]) or glob_large_float <= abs(arr_21_y_higher[1, m - 4]) or glob_large_float <= abs(arr_21_y_higher[1, m - 5]) then arr_21_ans[1] := glob_large_float; arr_21_ans[2] := glob_large_float; return else rm0 := arr_21_y_higher[1, m]/arr_21_y_higher[1, m - 1]; rm1 := arr_21_y_higher[1, m - 1]/arr_21_y_higher[1, m - 2]; rm2 := arr_21_y_higher[1, m - 2]/arr_21_y_higher[1, m - 3]; rm3 := arr_21_y_higher[1, m - 3]/arr_21_y_higher[1, m - 4]; rm4 := arr_21_y_higher[1, m - 4]/arr_21_y_higher[1, m - 5]; nr1 := ev(m - 1, float)*rm0 - 2.0*ev(m - 2, float)*rm1 + ev(m - 3, float)*rm2; nr2 := ev(m - 2, float)*rm1 - 2.0*ev(m - 3, float)*rm2 + ev(m - 4, float)*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 arr_21_ans[1] := glob_large_float; arr_21_ans[2] := glob_large_float; return 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) - 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; arr_21_ans[1] := rad_c; arr_21_ans[2] := ord_no; return end if end proc > which_radius := proc( > arr_22_pole,arr_22_real_pole,arr_22_complex_pole) > global ALWAYS,glob_display_flag, glob_large_float; > > if ((arr_22_real_pole[1] = glob_large_float) or (arr_22_real_pole[2] = glob_large_float)) and ((arr_22_complex_pole[1] <> glob_large_float) and (arr_22_complex_pole[2] <> glob_large_float)) and ((arr_22_complex_pole[1] > 0.0) and (arr_22_complex_pole[2] > 0.0)) then > arr_22_pole[1] := arr_22_complex_pole[1]; > arr_22_pole[2] := arr_22_complex_pole[2]; > if (glob_display_flag) then > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;; > return(); > fi;; > if ((arr_22_real_pole[1] <> glob_large_float) and (arr_22_real_pole[2] <> glob_large_float) and (arr_22_real_pole[1] > 0.0) and (arr_22_real_pole[2] > 0.0) and ((arr_22_complex_pole[1] = glob_large_float) or (arr_22_complex_pole[2] = glob_large_float) or (arr_22_complex_pole[1] <= 0.0 ) or (arr_22_complex_pole[2] <= 0.0))) then > arr_22_pole[1] := arr_22_real_pole[1]; > arr_22_pole[2] := arr_22_real_pole[2]; > if (glob_display_flag) then > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;; > return(); > fi;; > if (((arr_22_real_pole[1] = glob_large_float) or (arr_22_real_pole[2] = glob_large_float)) and ((arr_22_complex_pole[1] = glob_large_float) or (arr_22_complex_pole[2] = glob_large_float))) then > arr_22_pole[1] := glob_large_float; > arr_22_pole[2] := glob_large_float; > if (glob_display_flag) then > omniout_str(ALWAYS,"NO POLE"); > fi;; > return(); > fi;; > if ((arr_22_real_pole[1] < arr_22_complex_pole[1]) and (arr_22_real_pole[1] > 0.0) and (arr_22_real_pole[2] > 0.0)) then > arr_22_pole[1] := arr_22_real_pole[1]; > arr_22_pole[2] := arr_22_real_pole[2]; > if (glob_display_flag) then > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;; > return(); > fi;; > if ((arr_22_complex_pole[1] <> glob_large_float) and (arr_22_complex_pole[2] <> glob_large_float) and (arr_22_complex_pole[1] > 0.0) and (arr_22_complex_pole[2] > 0.0)) then > arr_22_pole[1] := arr_22_complex_pole[1]; > arr_22_pole[2] := arr_22_complex_pole[2]; > if (glob_display_flag) then > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;; > return(); > fi;; > arr_22_pole[1] := glob_large_float; > arr_22_pole[2] := glob_large_float; > if (glob_display_flag) then > omniout_str(ALWAYS,"NO POLE"); > fi; > > end; which_radius := proc(arr_22_pole, arr_22_real_pole, arr_22_complex_pole) global ALWAYS, glob_display_flag, glob_large_float; if (arr_22_real_pole[1] = glob_large_float or arr_22_real_pole[2] = glob_large_float) and arr_22_complex_pole[1] <> glob_large_float and arr_22_complex_pole[2] <> glob_large_float and 0. < arr_22_complex_pole[1] and 0. < arr_22_complex_pole[2] then arr_22_pole[1] := arr_22_complex_pole[1]; arr_22_pole[2] := arr_22_complex_pole[2]; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if; return end if; if arr_22_real_pole[1] <> glob_large_float and arr_22_real_pole[2] <> glob_large_float and 0. < arr_22_real_pole[1] and 0. < arr_22_real_pole[2] and ( arr_22_complex_pole[1] = glob_large_float or arr_22_complex_pole[2] = glob_large_float or arr_22_complex_pole[1] <= 0. or arr_22_complex_pole[2] <= 0.) then arr_22_pole[1] := arr_22_real_pole[1]; arr_22_pole[2] := arr_22_real_pole[2]; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if; return end if; if (arr_22_real_pole[1] = glob_large_float or arr_22_real_pole[2] = glob_large_float) and ( arr_22_complex_pole[1] = glob_large_float or arr_22_complex_pole[2] = glob_large_float) then arr_22_pole[1] := glob_large_float; arr_22_pole[2] := glob_large_float; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if; return end if; if arr_22_real_pole[1] < arr_22_complex_pole[1] and 0. < arr_22_real_pole[1] and 0. < arr_22_real_pole[2] then arr_22_pole[1] := arr_22_real_pole[1]; arr_22_pole[2] := arr_22_real_pole[2]; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if; return end if; if arr_22_complex_pole[1] <> glob_large_float and arr_22_complex_pole[2] <> glob_large_float and 0. < arr_22_complex_pole[1] and 0. < arr_22_complex_pole[2] then arr_22_pole[1] := arr_22_complex_pole[1]; arr_22_pole[2] := arr_22_complex_pole[2]; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if; return end if; arr_22_pole[1] := glob_large_float; arr_22_pole[2] := glob_large_float; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end proc > display_pole := proc( > arr_23_pole) > global ALWAYS,glob_display_flag, glob_large_float; > if ((arr_23_pole[1] <> glob_large_float) and glob_display_flag) then > omniout_float(ALWAYS,"Radius of convergence" ,4, arr_23_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole",4, arr_23_pole[2],4," "); > fi; > end; display_pole := proc(arr_23_pole) global ALWAYS, glob_display_flag, glob_large_float; if arr_23_pole[1] <> glob_large_float and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence", 4, arr_23_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole", 4, arr_23_pole[2], 4, " ") end if end proc > > 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 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;; > if (glob_max_iter < 2) then > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;; > if (errflag) then > > quit; > fi; > 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 > > 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 > sec_left := 0.0; > else > if (abs(sub2) > glob_small_float) then > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := -1.0; > fi; > fi;; > sec_left; > 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 glob_small_float < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := -1.0 end if end if; sec_left end proc > > 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 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;; > rrr > 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 > > wrk_prod := proc(fff,nnn) > local iii, ppp, rrr; > ppp := fff; > rrr := fff - 1; > iii := nnn; > while ((iii >= 1) and (rrr >= 1)) do > ppp := ppp * rrr; > rrr := rrr - 1; > iii := iii - 1; > od;; > ev(ppp,float); > end; wrk_prod := proc(fff, nnn) local iii, ppp, rrr; ppp := fff; rrr := fff - 1; iii := nnn; while 1 <= iii and 1 <= rrr do ppp := ppp*rrr; rrr := rrr - 1; iii := iii - 1 end do; ev(ppp, float) end proc > > factorial_1 := proc(nnn) > local ret; > ret := 1.0; > if (nnn > 1) then > ret := evalf( ev(nnn!,float)); > fi;; > ret; > end; factorial_1 := proc(nnn) local ret; ret := 1.0; if 1 < nnn then ret := evalf(ev(nnn!, float)) end if; ret end proc > > factorial_2 := proc(mmm2,nnn2) > local mmm, nnn, ret; > mmm := ev(mmm2,float); > nnn := ev(nnn2,float); > if (mmm < nnn) then > ret := evalf( 1.0 / ev(factorial_2(nnn,mmm),float)); > else > ret := 1.0; > if ((mmm = 0) and (nnn = 0)) then > ret := 1.0 ; > elif ( mmm = 0 ) then > ret := ev(factorial_1(nnn),float),numer; > elif ( mmm = nnn ) then > ret := 1.0; > else > ret := evalf( ev(wrk_prod(mmm,mmm-nnn),float)); > fi; > fi;; > ev(ret,float); > end; factorial_2 := proc(mmm2, nnn2) local mmm, nnn, ret; mmm := ev(mmm2, float); nnn := ev(nnn2, float); if mmm < nnn then ret := evalf(1.0/ev(factorial_2(nnn, mmm), float)) else ret := 1.0; if mmm = 0 and nnn = 0 then ret := 1.0 elif mmm = 0 then ret := ev(factorial_1(nnn), float), numer elif mmm = nnn then ret := 1.0 else ret := evalf(ev(wrk_prod(mmm, mmm - nnn), float)) end if end if; ev(ret, float) end proc > ev := proc(val,typ) > evalf(val); > end; ev := proc(val, typ) evalf(val) end proc > elapsed_real_time := proc() > time(); > end; elapsed_real_time := proc() time() end proc > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > sum_and_adjust := proc( > arr_33_higher,arr_33_higher_work,arr_33_higher_work2,order_d) > global glob_max_terms; > local ord,calc_term,jjj; > ord := order_d + 1; > jjj := 1; > while (ord >= 1) do > calc_term := jjj; > while (calc_term >= 1) do > adjust_subseries(arr_33_higher,arr_33_higher_work,ord,calc_term); > sum_subseries(arr_33_higher_work,arr_33_higher_work2,ord,calc_term); > calc_term := calc_term - 1; > od;; > ord := ord - 1; > jjj := jjj + 1; > od;; > end; sum_and_adjust := proc( arr_33_higher, arr_33_higher_work, arr_33_higher_work2, order_d) local ord, calc_term, jjj; global glob_max_terms; ord := order_d + 1; jjj := 1; while 1 <= ord do calc_term := jjj; while 1 <= calc_term do adjust_subseries(arr_33_higher, arr_33_higher_work, ord, calc_term); sum_subseries(arr_33_higher_work, arr_33_higher_work2, ord, calc_term); calc_term := calc_term - 1 end do; ord := ord - 1; jjj := jjj + 1 end do end proc > adjust_subseries := proc( > arr_34_higher,arr_34_higher_work,ord,calc_term) > global glob_max_terms,glob_h; > local iii; > iii := glob_max_terms; > while (iii >= calc_term) do > arr_34_higher_work[ord,iii] := arr_34_higher[ord,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;; > end; adjust_subseries := proc(arr_34_higher, arr_34_higher_work, ord, calc_term) local iii; global glob_max_terms, glob_h; iii := glob_max_terms; while calc_term <= iii do arr_34_higher_work[ord, iii] := arr_34_higher[ord, iii]/( glob_h^(calc_term - 1)*factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do end proc > sum_subseries := proc( > arr_35_higher_work,arr_35_higher_work2,ord,calc_term) > global glob_max_terms,glob_h; > local iii,temp_sum; > temp_sum := 0.0; > iii := glob_max_terms; > while (iii >= calc_term) do > temp_sum := temp_sum + arr_35_higher_work[ord,iii]; > iii := iii - 1; > od;; > arr_35_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / ((calc_term - 1)!); > end; sum_subseries := proc(arr_35_higher_work, arr_35_higher_work2, ord, calc_term) local iii, temp_sum; global glob_max_terms, glob_h; temp_sum := 0.; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + arr_35_higher_work[ord, iii]; iii := iii - 1 end do; arr_35_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/(calc_term - 1)! end proc #END ATS LIBRARY BLOCK #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > evalf(cos(x)); > end; exact_soln_y1 := proc(x) evalf(cos(x)) end proc > exact_soln_y2 := proc(x) > evalf(sin(x)); > end; exact_soln_y2 := proc(x) evalf(sin(x)) end proc > > #END USER DEF BLOCK #END OUTFILE5 > mainprog := proc() #BEGIN OUTFIEMAIN #BEGIN CONST DEF BLOCK > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, #END CONST DEF BLOCK > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > days_in_year, > glob_last_good_h, > glob_hmin_init, > sec_in_min, > glob_max_minutes, > glob_current_iter, > glob_progress_ind, > glob_max_order, > glob_large_float, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_clock_sec, > glob_almost_1, > years_in_century, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10abserr, > glob_iter, > glob_warned, > glob_log10_abserr, > glob_hmin, > glob_display_flag, > glob_log10relerr, > glob_start, > glob_look_poles, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > glob_small_float, > glob_log10_relerr, > glob_tot_order, > glob_smallish_float, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > glob_not_yet_start_msg, > djd_debug2, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_iter, > glob_abserr, > glob_h, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_normmax, > glob_max_sec, > glob_relerr, > glob_max_rel_trunc_err, > glob_last; > local dummy,hold,d1,d2,d3,d4,est_err_2,niii,done_once > ,arr_38_y2 > ,arr_38_m1 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y1_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_y2_var > ,x_start > ,x_end > ,it, jt, log10norm, max_terms, opt_iter, pole, tmp,arr_38_ans_complex,arr_38_ans_real,arr_38_norms,arr_38_old_pole,arr_38_pole; > dummy := 0; #BEGIN CONST BLOCK > Digits := 32; > printlevel := 1; > max_terms := 30; #END CONST BLOCK > glob_max_terms := max_terms; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > arr_38_y2 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_y2,glob_max_terms+1); > arr_38_m1 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_m1,glob_max_terms+1); > arr_38_y1 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_y1,glob_max_terms+1); > arr_38_x := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_x,glob_max_terms+1); > arr_38_tmp5 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp5,glob_max_terms+1); > arr_38_tmp4 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp4,glob_max_terms+1); > arr_38_tmp3 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp3,glob_max_terms+1); > arr_38_tmp2 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp2,glob_max_terms+1); > arr_38_tmp1 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp1,glob_max_terms+1); > arr_38_tmp0 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_tmp0,glob_max_terms+1); > arr_38_const_0D0 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_const_0D0,glob_max_terms+1); > arr_38_const_0D0[1] := 0.0; > arr_38_const_0 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_const_0,glob_max_terms+1); > arr_38_const_0[1] := 0; > arr_38_const_1 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_const_1,glob_max_terms+1); > arr_38_const_1[1] := 1; > arr_38_m1 := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_m1,glob_max_terms+1); > arr_38_m1[1] := -1.0; > arr_38_y1_init := Array(1..(glob_max_terms + 1),[]); > arr_38_y1_var := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_y1_init,glob_max_terms+1); > arr_38_y1_higher := Array(1..(2),1..(glob_max_terms + 1),[]); > it := 1; > while (it <= 2) do > jt := 1; > while (jt <= glob_max_terms ) do > arr_38_y1_higher[it,jt] := 0.0; > jt := jt + 1; > od;; > it := it + 1; > od;; > arr_38_y1_higher_work := Array(1..(2),1..(glob_max_terms + 1),[]); > arr_38_y1_higher_work2 := Array(1..(2),1..(glob_max_terms + 1),[]); > it := 1; > while (it <= 2) do > jt := 1; > while (jt <= glob_max_terms) do > arr_38_y1_higher_work[it,jt] := 0.0; > arr_38_y1_higher_work2[it,jt] := 0.0; > jt := jt + 1; > od;; > it := it + 1; > od;; > arr_38_pole := Array(1..(2 + 1),[]); > arr_38_old_pole := Array(1..(2 + 1),[]); > arr_38_ans_complex := Array(1..(2 + 1),[]); > arr_38_ans_real := Array(1..(2 + 1),[]); > arr_38_norms := Array(1..(glob_max_terms + 1),[]); > arr_38_y2_init := Array(1..(glob_max_terms + 1),[]); > arr_38_y2_var := Array(1..(glob_max_terms + 1),[]); > set_z(arr_38_y2_init,glob_max_terms+1); > arr_38_y2_higher := Array(1..(2),1..(glob_max_terms + 1),[]); > it := 1; > while (it <= 2) do > jt := 1; > while (jt <= glob_max_terms ) do > arr_38_y2_higher[it,jt] := 0.0; > jt := jt + 1; > od;; > it := it + 1; > od;; > arr_38_y2_higher_work := Array(1..(2),1..(glob_max_terms + 1),[]); > arr_38_y2_higher_work2 := Array(1..(2),1..(glob_max_terms + 1),[]); > it := 1; > while (it <= 2) do > jt := 1; > while (jt <= glob_max_terms) do > arr_38_y2_higher_work[it,jt] := 0.0; > arr_38_y2_higher_work2[it,jt] := 0.0; > jt := jt + 1; > od;; > it := it + 1; > od;; > arr_38_pole := Array(1..(2 + 1),[]); > arr_38_old_pole := Array(1..(2 + 1),[]); > arr_38_ans_complex := Array(1..(2 + 1),[]); > arr_38_ans_real := Array(1..(2 + 1),[]); > arr_38_norms := Array(1..(glob_max_terms + 1),[]); > glob_iolevel := 5; > INFO := 2; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_max_terms := 50; > ALWAYS := 1; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > days_in_year := 365.0; > glob_last_good_h := 0.1; > glob_hmin_init := 0.001; > sec_in_min := 60.0; > glob_max_minutes := 0.0; > glob_current_iter := 0; > glob_progress_ind := 1; > glob_max_order := 50; > glob_large_float := 9.0e100; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > years_in_century := 100.0; > djd_debug := true; > glob_dump := false; > glob_log10normmin := 0.1; > glob_log10abserr := 0.0; > glob_iter := 0; > glob_warned := false; > glob_log10_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_display_flag := true; > glob_log10relerr := 0.0; > glob_start := 0; > glob_look_poles := false; > glob_disp_incr := 0.1; > glob_initial_pass := true; > hours_in_day := 24.0; > glob_small_float := 0.1e-50; > glob_log10_relerr := 0.1e-10; > glob_tot_order := 0; > glob_smallish_float := 0.1e-100; > glob_max_hours := 0.0; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_optimal_done := false; > glob_not_yet_start_msg := true; > djd_debug2 := true; > glob_max_opt_iter := 10; > MAX_UNCHANGED := 10; > glob_unchanged_h_cnt := 0; > glob_no_eqs := 0; > glob_max_iter := 1000; > glob_abserr := 0.1e-10; > glob_h := 0.1; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > min_in_hour := 60.0; > glob_normmax := 0.0; > glob_max_sec := 10000.0; > glob_relerr := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > glob_orig_start_sec := elapsed_real_time(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 1; > glob_no_eqs := 2; > glob_tot_order := 0; > 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,"##############mtest2map.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * diff(y2,x,0) ;"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff(y1,x,0) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"printlevel := 1;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"arr_38_y1_init[1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"arr_38_y2_init[1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100000;"); > omniout_str(ALWAYS,"glob_progress_ind := 1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"evalf(cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x) "); > omniout_str(ALWAYS,"evalf(sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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_progress_ind := 1; > glob_log10_abserr := -8; > glob_log10_relerr := -8; > glob_hmax := 0.01; #BEGIN INPUT BLOCK > x_start := 0.1; > x_end := 10.0; > arr_38_y1_init[1] := exact_soln_y1(x_start); > arr_38_y2_init[1] := exact_soln_y2(x_start); > glob_h := 0.01 ; > glob_look_poles := true; > glob_max_iter := 100000; > glob_progress_ind := 1; #END INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := evalf( (60.0 * (glob_max_minutes + 60.0 * glob_max_hours))); > glob_abserr := 10.0 ^ glob_log10_abserr; > glob_relerr := 10.0 ^ glob_log10_relerr; > chk_data(); > glob_log10normmin := evalf( (log10(glob_large_float))); > if (abs(arr_38_y1_higher[1,1]) > glob_small_float) then #left paren 0001A > tmp := abs(arr_38_y1_higher[1,1]); > log10norm := evalf( (log10(tmp))); > if (log10norm < glob_log10normmin) then #left paren 0002A > glob_log10normmin := log10norm > fi;#right paren 0002A > fi;#right paren 0001A ; > if (abs(arr_38_y2_higher[1,1]) > glob_small_float) then #left paren 0001A > tmp := abs(arr_38_y2_higher[1,1]); > log10norm := evalf( (log10(tmp))); > if (log10norm < glob_log10normmin) then #left paren 0002A > glob_log10normmin := log10norm > fi;#right paren 0002A > fi;#right paren 0001A ; > glob_hmax := glob_h; > omniout_str(INFO," "); > omniout_str(INFO,"TOP Optimize Loop"); > glob_clock_sec := elapsed_real_time(); > glob_current_iter := 0; > omniout_str(DEBUGL,"Before OPTIMIZE H Loop"); > done_once := false; > while (not done_once) and (glob_current_iter < glob_max_iter) and ((glob_clock_sec - glob_orig_start_sec) < glob_max_sec) and (not glob_optimal_done) and (glob_iter < glob_max_iter) do #left paren 0001B > glob_clock_start_sec := elapsed_real_time(); > omniout_str(DEBUGL,"Entered OPTIMIZE H Loop"); > done_once := true; > glob_clock_sec := elapsed_real_time(); > glob_current_iter := glob_current_iter + 1; #Start Series -- INITIALIZE > arr_38_x[1] := x_start; > arr_38_x[2] := (glob_h); > start_all_series(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > display_alot(glob_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > opt_iter := 1; > while (opt_iter < 5) and ((glob_clock_sec - glob_orig_start_sec) < glob_max_sec) and (not glob_optimal_done) and (glob_iter < glob_max_iter) and (glob_h <= glob_hmax) do > opt_iter := opt_iter + 1; > sub_iter := 1; > while sub_iter <= 2 do > atomall(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > sub_iter := sub_iter + 1; > od; > arr_38_x[1] := evalf(arr_38_x[1] + glob_h); > arr_38_x[2] := glob_h; > #Jump Series In Optimize -- JUMP IN OPTIMIZE > jump_all_series(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > > glob_optimal_clock_start_sec := elapsed_real_time(); > if (glob_max_trunc_err < glob_max_rel_trunc_err * glob_normmax) then > glob_max_trunc_err := glob_max_rel_trunc_err * glob_normmax / 100.0; > else > glob_max_trunc_err := glob_max_rel_trunc_err / 100.0; > fi;; > set_z(arr_38_norms,glob_max_terms+1); > niii := 1; > while (niii <= glob_max_terms) do > if (abs(arr_38_y1[niii]) > arr_38_norms[niii]) then > arr_38_norms[niii] := abs(arr_38_y1[niii]); > fi;; > niii := niii + 1; > od; > ; > niii := 1; > while (niii <= glob_max_terms) do > if (abs(arr_38_y2[niii]) > arr_38_norms[niii]) then > arr_38_norms[niii] := abs(arr_38_y2[niii]); > fi;; > niii := niii + 1; > od; > d1 := arr_38_norms[glob_max_terms - 4 - glob_max_order]; > d2 := arr_38_norms[glob_max_terms - 5 - glob_max_order]; > d3 := arr_38_norms[glob_max_terms - 6 - glob_max_order]; > d4 := arr_38_norms[glob_max_terms - 7 - glob_max_order]; > est_err_2 := evalf((abs(d1) + abs(d2) + abs(d3) + abs(d4))); > if (est_err_2 < glob_max_trunc_err) and (glob_h < glob_hmax) and (opt_iter >= 5) then > glob_h := 2.0 * glob_h; > opt_iter := 0; > elif est_err_2 >= glob_max_trunc_err then > glob_h := glob_h/2.0; > glob_optimal_done := true; > opt_iter := 5; > fi; > display_alot(opt_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > od;;#end FIRST OPIMIZE loop right paren 0001B1 > omniout_str(DEBUGL,"Try another point Optimizing "); > od;;#end SECOND OPIMIZE loop right paren 0001B2 > omniout_str(DEBUGL,"Finished Optimizing "); > if (glob_iter >= glob_max_iter) then > omniout_str(DEBUGL,"Maximum Iterations Reached before Optimized!"); > fi;; > if ((elapsed_real_time() - glob_orig_start_sec) >= glob_max_sec ) then > omniout_str(ALWAYS,"Maximum Time Reached before Opimized!"); > fi;; > omniout_int(INFO,"Iterations",30,glob_iter,4," "); #Start Series -- INITIALIZE FOR SOLUTION > arr_38_x[1] := evalf(x_start); > arr_38_x[2] := glob_h; > start_all_series(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); #Jump Series In Solve -- JUMP IN SOLVE > glob_clock_start_sec := elapsed_real_time(); > start_arr_38_y1(); > if (abs(arr_38_y1_higher[1,1]) > glob_small_float) then > tmp := abs(arr_38_y1_higher[1,1]); > log10norm := evalf( (log10(tmp))); > if (log10norm < glob_log10normmin) then > glob_log10normmin := log10norm; > fi; > fi;; > display_alot(opt_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > start_arr_38_y2(); > if (abs(arr_38_y2_higher[1,1]) > glob_small_float) then > tmp := abs(arr_38_y2_higher[1,1]); > log10norm := evalf( (log10(tmp))); > if (log10norm < glob_log10normmin) then > glob_log10normmin := log10norm; > fi; > fi;; > display_alot(opt_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > glob_clock_sec := elapsed_real_time(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_real_time(); > while ((glob_current_iter < glob_max_iter) and (arr_38_x[1] <= x_end ) and ((glob_clock_sec - glob_orig_start_sec) < glob_max_sec)) do #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_real_time(); > glob_current_iter := glob_current_iter + 1; > sub_iter := 1; > while sub_iter <= 2 do > atomall(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > sub_iter := sub_iter + 1; > od; > arr_38_pole := Array(1..(2 + 1),[]); > set_z(arr_38_pole,2); > if (glob_look_poles) then #left paren 0004C > check_for_pole(arr_38_pole > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > display_pole(arr_38_pole); > adjust_for_for_pole( > arr_38_pole,glob_h > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > fi;;#was right paren 0004C > arr_38_x[1] := evalf(arr_38_x[1] + glob_h); > arr_38_x[2] := glob_h; > jump_all_series(dummy > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > > > if ((opt_iter mod glob_progress_ind) = 0) then > display_alot(glob_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); > fi;; > od;;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;; > if (elapsed_real_time() - glob_orig_start_sec >= glob_max_sec ) then > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi; > glob_clock_sec := elapsed_real_time(); > omniout_int(INFO,"Iterations",5,glob_iter,4," "); > prog_report(glob_iter,opt_iter > ,arr_38_norms > ,x_start > ,x_end > ,arr_38_y2 > ,arr_38_y1 > ,arr_38_x > ,arr_38_tmp5 > ,arr_38_tmp4 > ,arr_38_tmp3 > ,arr_38_tmp2 > ,arr_38_tmp1 > ,arr_38_tmp0 > ,arr_38_y1_var > ,arr_38_y1_init > ,arr_38_y1_higher > ,arr_38_y1_higher_work > ,arr_38_y1_higher_work2 > ,arr_38_y2_var > ,arr_38_y2_init > ,arr_38_y2_higher > ,arr_38_y2_higher_work > ,arr_38_y2_higher_work2 > ,arr_38_const_0D0 > ,arr_38_const_0 > ,arr_38_const_1 > , arr_38_m1 > ); #END OUTFILEMAIN > end; Warning, `sub_iter` is implicitly declared local to procedure `mainprog` mainprog := proc() local dummy, hold, d1, d2, d3, d4, est_err_2, niii, done_once, arr_38_y2, arr_38_m1, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y1_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_y2_var, x_start, x_end, it, jt, log10norm, max_terms, opt_iter, pole, tmp, arr_38_ans_complex, arr_38_ans_real, arr_38_norms, arr_38_old_pole, arr_38_pole, sub_iter; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, days_in_year, glob_last_good_h, glob_hmin_init, sec_in_min, glob_max_minutes, glob_current_iter, glob_progress_ind, glob_max_order, glob_large_float, glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, glob_almost_1, years_in_century, djd_debug, glob_dump, glob_log10normmin, glob_log10abserr, glob_iter, glob_warned, glob_log10_abserr, glob_hmin, glob_display_flag, glob_log10relerr, glob_start, glob_look_poles, glob_disp_incr, glob_initial_pass, hours_in_day, glob_small_float, glob_log10_relerr, glob_tot_order, glob_smallish_float, glob_max_hours, glob_dump_analytic, glob_hmax, glob_optimal_done, glob_not_yet_start_msg, djd_debug2, glob_max_opt_iter, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_no_eqs, glob_max_iter, glob_abserr, glob_h, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_normmax, glob_max_sec, glob_relerr, glob_max_rel_trunc_err, glob_last; dummy := 0; Digits := 32; printlevel := 1; max_terms := 30; glob_max_terms := max_terms; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; arr_38_y2 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_y2, glob_max_terms + 1); arr_38_m1 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_m1, glob_max_terms + 1); arr_38_y1 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_y1, glob_max_terms + 1); arr_38_x := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_x, glob_max_terms + 1); arr_38_tmp5 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp5, glob_max_terms + 1); arr_38_tmp4 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp4, glob_max_terms + 1); arr_38_tmp3 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp3, glob_max_terms + 1); arr_38_tmp2 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp2, glob_max_terms + 1); arr_38_tmp1 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp1, glob_max_terms + 1); arr_38_tmp0 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_tmp0, glob_max_terms + 1); arr_38_const_0D0 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_const_0D0, glob_max_terms + 1); arr_38_const_0D0[1] := 0.; arr_38_const_0 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_const_0, glob_max_terms + 1); arr_38_const_0[1] := 0; arr_38_const_1 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_const_1, glob_max_terms + 1); arr_38_const_1[1] := 1; arr_38_m1 := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_m1, glob_max_terms + 1); arr_38_m1[1] := -1.0; arr_38_y1_init := Array(1 .. glob_max_terms + 1, []); arr_38_y1_var := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_y1_init, glob_max_terms + 1); arr_38_y1_higher := Array(1 .. 2, 1 .. glob_max_terms + 1, []); it := 1; while it <= 2 do jt := 1; while jt <= glob_max_terms do arr_38_y1_higher[it, jt] := 0.; jt := jt + 1 end do; it := it + 1 end do; arr_38_y1_higher_work := Array(1 .. 2, 1 .. glob_max_terms + 1, []); arr_38_y1_higher_work2 := Array(1 .. 2, 1 .. glob_max_terms + 1, []); it := 1; while it <= 2 do jt := 1; while jt <= glob_max_terms do arr_38_y1_higher_work[it, jt] := 0.; arr_38_y1_higher_work2[it, jt] := 0.; jt := jt + 1 end do; it := it + 1 end do; arr_38_pole := Array(1 .. 3, []); arr_38_old_pole := Array(1 .. 3, []); arr_38_ans_complex := Array(1 .. 3, []); arr_38_ans_real := Array(1 .. 3, []); arr_38_norms := Array(1 .. glob_max_terms + 1, []); arr_38_y2_init := Array(1 .. glob_max_terms + 1, []); arr_38_y2_var := Array(1 .. glob_max_terms + 1, []); set_z(arr_38_y2_init, glob_max_terms + 1); arr_38_y2_higher := Array(1 .. 2, 1 .. glob_max_terms + 1, []); it := 1; while it <= 2 do jt := 1; while jt <= glob_max_terms do arr_38_y2_higher[it, jt] := 0.; jt := jt + 1 end do; it := it + 1 end do; arr_38_y2_higher_work := Array(1 .. 2, 1 .. glob_max_terms + 1, []); arr_38_y2_higher_work2 := Array(1 .. 2, 1 .. glob_max_terms + 1, []); it := 1; while it <= 2 do jt := 1; while jt <= glob_max_terms do arr_38_y2_higher_work[it, jt] := 0.; arr_38_y2_higher_work2[it, jt] := 0.; jt := jt + 1 end do; it := it + 1 end do; arr_38_pole := Array(1 .. 3, []); arr_38_old_pole := Array(1 .. 3, []); arr_38_ans_complex := Array(1 .. 3, []); arr_38_ans_real := Array(1 .. 3, []); arr_38_norms := Array(1 .. glob_max_terms + 1, []); glob_iolevel := 5; INFO := 2; DEBUGMASSIVE := 4; DEBUGL := 3; glob_max_terms := 50; ALWAYS := 1; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_warned2 := false; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); days_in_year := 365.0; glob_last_good_h := 0.1; glob_hmin_init := 0.001; sec_in_min := 60.0; glob_max_minutes := 0.; glob_current_iter := 0; glob_progress_ind := 1; glob_max_order := 50; glob_large_float := 0.90*10^101; glob_reached_optimal_h := false; glob_not_yet_finished := true; glob_clock_sec := 0.; glob_almost_1 := 0.9990; years_in_century := 100.0; djd_debug := true; glob_dump := false; glob_log10normmin := 0.1; glob_log10abserr := 0.; glob_iter := 0; glob_warned := false; glob_log10_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_display_flag := true; glob_log10relerr := 0.; glob_start := 0; glob_look_poles := false; glob_disp_incr := 0.1; glob_initial_pass := true; hours_in_day := 24.0; glob_small_float := 0.1*10^(-50); glob_log10_relerr := 0.1*10^(-10); glob_tot_order := 0; glob_smallish_float := 0.1*10^(-100); glob_max_hours := 0.; glob_dump_analytic := false; glob_hmax := 1.0; glob_optimal_done := false; glob_not_yet_start_msg := true; djd_debug2 := true; glob_max_opt_iter := 10; MAX_UNCHANGED := 10; glob_unchanged_h_cnt := 0; glob_no_eqs := 0; glob_max_iter := 1000; glob_abserr := 0.1*10^(-10); glob_h := 0.1; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; min_in_hour := 60.0; glob_normmax := 0.; glob_max_sec := 10000.0; glob_relerr := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); glob_orig_start_sec := elapsed_real_time(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 1; glob_no_eqs := 2; glob_tot_order := 0; 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, "##############mtest2map.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff(y2,x,0) ;"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff(y1,x,0) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "printlevel := 1;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "arr_38_y1_init[1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "arr_38_y2_init[1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100000;"); omniout_str(ALWAYS, "glob_progress_ind := 1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "evalf(cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x) "); omniout_str(ALWAYS, "evalf(sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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_progress_ind := 1; glob_log10_abserr := -8; glob_log10_relerr := -8; glob_hmax := 0.01; x_start := 0.1; x_end := 10.0; arr_38_y1_init[1] := exact_soln_y1(x_start); arr_38_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 100000; glob_progress_ind := 1; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := evalf(60.0*(glob_max_minutes + 60.0*glob_max_hours)); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); glob_log10normmin := evalf(log10(glob_large_float)); if glob_small_float < abs(arr_38_y1_higher[1, 1]) then tmp := abs(arr_38_y1_higher[1, 1]); log10norm := evalf(log10(tmp)); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; if glob_small_float < abs(arr_38_y2_higher[1, 1]) then tmp := abs(arr_38_y2_higher[1, 1]); log10norm := evalf(log10(tmp)); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; glob_hmax := glob_h; omniout_str(INFO, " "); omniout_str(INFO, "TOP Optimize Loop"); glob_clock_sec := elapsed_real_time(); glob_current_iter := 0; omniout_str(DEBUGL, "Before OPTIMIZE H Loop"); done_once := false; while not done_once and glob_current_iter < glob_max_iter and glob_clock_sec - glob_orig_start_sec < glob_max_sec and not glob_optimal_done and glob_iter < glob_max_iter do glob_clock_start_sec := elapsed_real_time(); omniout_str(DEBUGL, "Entered OPTIMIZE H Loop"); done_once := true; glob_clock_sec := elapsed_real_time(); glob_current_iter := glob_current_iter + 1; arr_38_x[1] := x_start; arr_38_x[2] := glob_h; start_all_series(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); display_alot(glob_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); opt_iter := 1; while opt_iter < 5 and glob_clock_sec - glob_orig_start_sec < glob_max_sec and not glob_optimal_done and glob_iter < glob_max_iter and glob_h <= glob_hmax do opt_iter := opt_iter + 1; sub_iter := 1; while sub_iter <= 2 do atomall(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); sub_iter := sub_iter + 1 end do; arr_38_x[1] := evalf(arr_38_x[1] + glob_h); arr_38_x[2] := glob_h; jump_all_series(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); glob_optimal_clock_start_sec := elapsed_real_time(); if glob_max_trunc_err < glob_max_rel_trunc_err*glob_normmax then glob_max_trunc_err := glob_max_rel_trunc_err*glob_normmax/100.0 else glob_max_trunc_err := glob_max_rel_trunc_err/100.0 end if; set_z(arr_38_norms, glob_max_terms + 1); niii := 1; while niii <= glob_max_terms do if arr_38_norms[niii] < abs(arr_38_y1[niii]) then arr_38_norms[niii] := abs(arr_38_y1[niii]) end if; niii := niii + 1 end do; niii := 1; while niii <= glob_max_terms do if arr_38_norms[niii] < abs(arr_38_y2[niii]) then arr_38_norms[niii] := abs(arr_38_y2[niii]) end if; niii := niii + 1 end do; d1 := arr_38_norms[glob_max_terms - 4 - glob_max_order]; d2 := arr_38_norms[glob_max_terms - 5 - glob_max_order]; d3 := arr_38_norms[glob_max_terms - 6 - glob_max_order]; d4 := arr_38_norms[glob_max_terms - 7 - glob_max_order]; est_err_2 := evalf(abs(d1) + abs(d2) + abs(d3) + abs(d4)); if est_err_2 < glob_max_trunc_err and glob_h < glob_hmax and 5 <= opt_iter then glob_h := 2.0*glob_h; opt_iter := 0 elif glob_max_trunc_err <= est_err_2 then glob_h := glob_h/2.0; glob_optimal_done := true; opt_iter := 5 end if; display_alot(opt_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1) end do; omniout_str(DEBUGL, "Try another point Optimizing ") end do; omniout_str(DEBUGL, "Finished Optimizing "); if glob_max_iter <= glob_iter then omniout_str(DEBUGL, "Maximum Iterations Reached before Optimized!") end if; if glob_max_sec <= elapsed_real_time() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Opimized!") end if; omniout_int(INFO, "Iterations", 30, glob_iter, 4, " "); arr_38_x[1] := evalf(x_start); arr_38_x[2] := glob_h; start_all_series(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); glob_clock_start_sec := elapsed_real_time(); start_arr_38_y1(); if glob_small_float < abs(arr_38_y1_higher[1, 1]) then tmp := abs(arr_38_y1_higher[1, 1]); log10norm := evalf(log10(tmp)); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(opt_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); start_arr_38_y2(); if glob_small_float < abs(arr_38_y2_higher[1, 1]) then tmp := abs(arr_38_y2_higher[1, 1]); log10norm := evalf(log10(tmp)); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(opt_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); glob_clock_sec := elapsed_real_time(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_real_time(); while glob_current_iter < glob_max_iter and arr_38_x[1] <= x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_real_time(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 2 do atomall(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); sub_iter := sub_iter + 1 end do; arr_38_pole := Array(1 .. 3, []); set_z(arr_38_pole, 2); if glob_look_poles then check_for_pole(arr_38_pole, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1) ; display_pole(arr_38_pole); adjust_for_for_pole(arr_38_pole, glob_h, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1) end if; arr_38_x[1] := evalf(arr_38_x[1] + glob_h); arr_38_x[2] := glob_h; jump_all_series(dummy, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1); if opt_iter mod glob_progress_ind = 0 then display_alot(glob_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1) end if 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 glob_max_sec <= elapsed_real_time() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_real_time(); omniout_int(INFO, "Iterations", 5, glob_iter, 4, " "); prog_report(glob_iter, opt_iter, arr_38_norms, x_start, x_end, arr_38_y2, arr_38_y1, arr_38_x, arr_38_tmp5, arr_38_tmp4, arr_38_tmp3, arr_38_tmp2, arr_38_tmp1, arr_38_tmp0, arr_38_y1_var, arr_38_y1_init, arr_38_y1_higher, arr_38_y1_higher_work, arr_38_y1_higher_work2, arr_38_y2_var, arr_38_y2_init, arr_38_y2_higher, arr_38_y2_higher_work, arr_38_y2_higher_work2, arr_38_const_0D0, arr_38_const_0, arr_38_const_1, arr_38_m1) end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############mtest2map.ode################# diff ( y1 , x , 1 ) = m1 * diff(y2,x,0) ; diff ( y2 , x , 1 ) = diff(y1,x,0) ; ! Digits := 32; printlevel := 1; max_terms := 30; ! x_start := 0.1; x_end := 10.0; arr_38_y1_init[1] := exact_soln_y1(x_start); arr_38_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.01 ; glob_look_poles := true; glob_max_iter := 100000; glob_progress_ind := 1; ! exact_soln_y1 := proc(x) evalf(cos(x)); end; exact_soln_y2 := proc(x) evalf(sin(x)); end; #######END OF ECHO OF PROBLEM################# TOP Optimize Loop Before OPTIMIZE H Loop Entered OPTIMIZE H Loop x[1] = = 0.11 y1(analytic)= = 0.99395609795669685035783961141985 y1(numeric) = = 0.99395609795664910495392795036316 absolute error = 4.774540391166105669e-14 relative error = 4.8035727141080586207702100995819e-12 % glob_h = 0.01 y2(analytic)= = 0.10977830083717480866494949008345 y2(numeric) = = 0.10977830083716652761856889027883 absolute error = 8.28104638059980462e-15 relative error = 7.5434273599136906409218485316196e-12 % glob_h = 0.01 x[1] = = 0.12 y1(analytic)= = 0.99280863585386625224809816785763 y1(numeric) = = 0.99280863585377093183294272848961 absolute error = 9.532041515543936802e-14 relative error = 9.6010864242189967651137837390795e-12 % glob_h = 0.01 y2(analytic)= = 0.11971220728891935996735061427097 y2(numeric) = = 0.1197122072889018438105239742794 absolute error = 1.751615682663999157e-14 relative error = 1.4631888612967959598537278554674e-11 % glob_h = 0.01 x[1] = = 0.13 y1(analytic)= = 0.99156189371478803959451217115181 y1(numeric) = = 0.99156189371464532885872395939496 absolute error = 1.4271073578821175685e-13 relative error = 1.4392519185419699374860352628140e-11 % glob_h = 0.01 y2(analytic)= = 0.12963414261969485954120581070831 y2(numeric) = = 0.1296341426196671568372693190888 absolute error = 2.770270393649161951e-14 relative error = 2.1369913339699787618812640696549e-11 % glob_h = 0.01 x[1] = = 0.14 y1(analytic)= = 0.9902159962126371718989482270114 y1(numeric) = = 0.99021599621244726979509674584486 absolute error = 1.8990210385148116654e-13 relative error = 1.9177846508016008266365509271423e-11 % glob_h = 0.01 y2(analytic)= = 0.13954311464423648171798835170537 y2(numeric) = = 0.13954311464419764384814073164673 absolute error = 3.883786984762005864e-14 relative error = 2.7832164952485651398147396235099e-11 % glob_h = 0.01 Try another point Optimizing Finished Optimizing Iterations = -1 x[1] = = 0.1 y1(analytic)= = 0.99500416527802576609556198780387 y1(numeric) = = 0.99500416527802576609556198780387 absolute error = 0 relative error = 0 % glob_h = 0.01 y2(analytic)= = 0.099833416646828152306814198410622 y2(numeric) = = 0.099833416646828152306814198410622 absolute error = 0 relative error = 0 % glob_h = 0.01 x[1] = = 0.1 y1(analytic)= = 0.99500416527802576609556198780387 y1(numeric) = = 0.99500416527802576609556198780387 absolute error = 0 relative error = 0 % glob_h = 0.01 y2(analytic)= = 0.099833416646828152306814198410622 y2(numeric) = = 0.099833416646828152306814198410622 absolute error = 0 relative error = 0 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.11 y1(analytic)= = 0.99395609795669685035783961141985 y1(numeric) = = 0.99395609795664910495392795036316 absolute error = 4.774540391166105669e-14 relative error = 4.8035727141080586207702100995819e-12 % glob_h = 0.01 y2(analytic)= = 0.10977830083717480866494949008345 y2(numeric) = = 0.10977830083716652761856889027883 absolute error = 8.28104638059980462e-15 relative error = 7.5434273599136906409218485316196e-12 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.12 y1(analytic)= = 0.99280863585386625224809816785763 y1(numeric) = = 0.99280863585377093183294272848961 absolute error = 9.532041515543936802e-14 relative error = 9.6010864242189967651137837390795e-12 % glob_h = 0.01 y2(analytic)= = 0.11971220728891935996735061427097 y2(numeric) = = 0.1197122072889018438105239742794 absolute error = 1.751615682663999157e-14 relative error = 1.4631888612967959598537278554674e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.13 y1(analytic)= = 0.99156189371478803959451217115181 y1(numeric) = = 0.99156189371464532885872395939496 absolute error = 1.4271073578821175685e-13 relative error = 1.4392519185419699374860352628140e-11 % glob_h = 0.01 y2(analytic)= = 0.12963414261969485954120581070831 y2(numeric) = = 0.1296341426196671568372693190888 absolute error = 2.770270393649161951e-14 relative error = 2.1369913339699787618812640696549e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.14 y1(analytic)= = 0.9902159962126371718989482270114 y1(numeric) = = 0.99021599621244726979509674584486 absolute error = 1.8990210385148116654e-13 relative error = 1.9177846508016008266365509271423e-11 % glob_h = 0.01 y2(analytic)= = 0.13954311464423648171798835170537 y2(numeric) = = 0.13954311464419764384814073164673 absolute error = 3.883786984762005864e-14 relative error = 2.7832164952485651398147396235099e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.15 y1(analytic)= = 0.98877107793604228673498099865434 y1(numeric) = = 0.98877107793580540643923114937185 absolute error = 2.3688029574984928249e-13 relative error = 2.3957041324905304146382510150540e-11 % glob_h = 0.01 y2(analytic)= = 0.14943813247359922149772543868764 y2(numeric) = = 0.14943813247354830285102714965985 absolute error = 5.091864669828902779e-14 relative error = 3.4073396030484166820146081284624e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=3.0MB, time=0.18 NO POLE x[1] = = 0.16 y1(analytic)= = 0.98722728337562694904095252401834 y1(numeric) = = 0.98722728337534331791232871792789 absolute error = 2.8363112862380609045e-13 relative error = 2.8730073955612933581508588929589e-11 % glob_h = 0.01 y2(analytic)= = 0.15931820661424596331146315968599 y2(numeric) = = 0.15931820661418202147434538156062 absolute error = 6.394183711777812537e-14 relative error = 4.0134670403740632458956166981409e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.17 y1(analytic)= = 0.9855847669095607091719299902125 y1(numeric) = = 0.98558476690923056870921348616136 absolute error = 3.3014046271650405114e-13 relative error = 3.3496912066904786167683423278497e-11 % glob_h = 0.01 y2(analytic)= = 0.16918234906699601015762437667085 y2(numeric) = = 0.1691823490669181061028793307814 absolute error = 7.790405474504588945e-14 relative error = 4.6047389207367002511184882561002e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.18 y1(analytic)= = 0.98384369278812141459271602461153 y1(numeric) = = 0.98384369278774502038898183924493 absolute error = 3.7639420373418536660e-13 relative error = 3.8257520629879655092985268679294e-11 % glob_h = 0.01 y2(analytic)= = 0.17902957342582417834180273969921 y2(numeric) = = 0.17902957342573137661702697307071 absolute error = 9.280172477576662850e-14 relative error = 5.1835974917415746851192810871992e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.19 y1(analytic)= = 0.98200423511727031896787750418991 y1(numeric) = = 0.98200423511684794066267757253803 absolute error = 4.2237830519993165188e-13 relative error = 4.3011861873435963773312927978406e-11 % glob_h = 0.01 y2(analytic)= = 0.18885889497650057799285115298131 y2(numeric) = = 0.18885889497639194690831348750208 absolute error = 1.0863108453766547923e-13 relative error = 5.7519707796226530978228040837835e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.2 y1(analytic)= = 0.98006657784124163112419651674817 y1(numeric) = = 0.98006657784077355235339611054142 absolute error = 4.6807877080040620675e-13 relative error = 4.7759895233997974105008995715284e-11 % glob_h = 0.01 y2(analytic)= = 0.19866933079506121545941262711839 y2(numeric) = = 0.19866933079493582727531855474524 absolute error = 1.2538818409407237315e-13 relative error = 6.3114011403912897354039409547893e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.21 y1(analytic)= = 0.97803091472414824491613856809935 y1(numeric) = = 0.97803091472363476325941330809417 absolute error = 5.1348165672526000518e-13 relative error = 5.2501577301376667384032308491468e-11 % glob_h = 0.01 y2(analytic)= = 0.20845989984609957060871242622764 y2(numeric) = = 0.20845989984595650172183681439967 absolute error = 1.4306888687561182797e-13 relative error = 6.8631370820592258923667493150923e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.22 y1(analytic)= = 0.9758974493306054894060229810447 y1(numeric) = = 0.97589744933004691633202410755843 absolute error = 5.5857307399887348627e-13 relative error = 5.7236861760630063838359326994125e-11 % glob_h = 0.01 y2(analytic)= = 0.21822962308086931995179100545701 y2(numeric) = = 0.21822962308070765108145106373133 absolute error = 1.6166887033994172568e-13 relative error = 7.4082000444106580211692074480185e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.23 y1(analytic)= = 0.9736663950053748369677306480716 y1(numeric) = = 0.97366639500477149777692654083383 absolute error = 6.0333919080410723777e-13 relative error = 6.1965699329776774565081948370508e-11 % glob_h = 0.01 y2(analytic)= = 0.22797752353518839540461721236007 y2(numeric) = = 0.22797752353500721177795776186433 absolute error = 1.8118362665945049574e-13 relative error = 7.9474337579373148856654673065212e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.24 y1(analytic)= = 0.97133797485202960492617524696338 y1(numeric) = = 0.97133797485138183869137751124996 absolute error = 6.4776623479773571342e-13 relative error = 6.6688037693205010981025077501000e-11 % glob_h = 0.01 y2(analytic)= = 0.23770262642713458836079208448982 y2(numeric) = = 0.23770262642693297989735526610012 absolute error = 2.0160846343681838970e-13 relative error = 8.4815412630124846031700541591826e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.25 y1(analytic)= = 0.96891242171064478414459544949419 y1(numeric) = = 0.968912421709952943649178210277 absolute error = 6.9184049541723921719e-13 relative error = 7.1403821430607058397228461519604e-11 % glob_h = 0.01 y2(analytic)= = 0.24740395925452292959684870484939 y2(numeric) = = 0.24740395925429999109240036003563 absolute error = 2.2293850444834481376e-13 relative error = 9.0111130444356116653811098358284e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.26 y1(analytic)= = 0.96638997813451322555821764645006 y1(numeric) = = 0.96638997813377767723203901592923 absolute error = 7.3554832617863052083e-13 relative error = 7.6112991941256294806168809428973e-11 % glob_h = 0.01 y2(analytic)= = 0.25708055189215509735338846436522 y2(numeric) = = 0.25708055189190992866297352438696 absolute error = 2.4516869041493997826e-13 relative error = 9.5366486733616424254201203886486e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.27 y1(analytic)= = 0.9637708963658905130162327094922 y1(numeric) = = 0.96377089636511163686926771583547 absolute error = 7.7887614696499365673e-13 relative error = 8.0815487363430141951430823859291e-11 % glob_h = 0.01 y2(analytic)= = 0.26673143668883112873228652102054 y2(numeric) = = 0.26673143668856283495248584559218 absolute error = 2.6829377980067542836e-13 relative error = 1.0058573639884335379957424941520e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.28 y1(analytic)= = 0.96105543831077094792459005359648 y1(numeric) = = 0.96105543830994913747828463995187 absolute error = 8.2181044630541364461e-13 relative error = 8.5511242488767806727249534136103e-11 % glob_h = 0.01 y2(analytic)= = 0.27635564856411373331966955845785 y2(numeric) = = 0.27635564856382142497003077411861 absolute error = 2.9230834963878433924e-13 relative error = 1.0577252578608670056983823708530e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.29 y1(analytic)= = 0.95824387551269716807012477793186 y1(numeric) = = 0.958243875511832830286480800763 absolute error = 8.6433778364397716886e-13 relative error = 9.0200188671336235355342042919445e-11 % glob_h = 0.01 y2(analytic)= = 0.28595222510483553268394020550437 y2(numeric) = = 0.28595222510451832588755520671287 absolute error = 3.1720679638499879150e-13 relative error = 1.1092999757868809645810602174954e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=0.40 NO POLE NO POLE x[1] = = 0.3 y1(analytic)= = 0.95533648912560601964231022756805 y1(numeric) = = 0.95533648912469957485071170204541 absolute error = 9.0644479159852552264e-13 relative error = 9.4882253731161283046247271523821e-11 % glob_h = 0.01 y2(analytic)= = 0.29552020666133957510532074568503 y2(numeric) = = 0.29552020666099659176852263809543 absolute error = 3.4298333679810758960e-13 relative error = 1.1606087471072996407038908111932e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.31 y1(analytic)= = 0.95233356988571339784280543620221 y1(numeric) = = 0.9523335698847652796645965937271 absolute error = 9.4811817820884247511e-13 relative error = 9.9557361851963614090381403389158e-11 % glob_h = 0.01 y2(analytic)= = 0.30505863644344350156564332395896 y2(numeric) = = 0.30505863644307386955679570941135 absolute error = 3.6963200884761454761e-13 relative error = 1.2116752803887349005057726725063e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.32 y1(analytic)= = 0.94923541808244086757530727376609 y1(numeric) = = 0.94923541808145152284613331266634 absolute error = 9.8934472917396109975e-13 relative error = 1.0422543347282020066394976397079e-10 % glob_h = 0.01 y2(analytic)= = 0.31456656061611776666175754341715 y2(numeric) = = 0.31456656061572061998910916987342 absolute error = 3.9714667264837354373e-13 relative error = 1.2625203132542516533311358344461e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.33 y1(analytic)= = 0.94604234352838697152941057836621 y1(numeric) = = 0.94604234352735686021933230334278 absolute error = 1.03011131007827502343e-12 relative error = 1.0888638517345238429820955793842e-10 % glob_h = 0.01 y2(analytic)= = 0.32404302839486834670019569617022 y2(numeric) = = 0.32404302839444282568877362313292 absolute error = 4.2552101142207303730e-13 relative error = 1.3131620622417677964457660658130e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.34 y1(analytic)= = 0.94275466552834622850264406002658 y1(numeric) = = 0.94275466552727582363403791900823 absolute error = 1.07040486860614101835e-12 relative error = 1.1354012955282019485108127425053e-10 % glob_h = 0.01 y2(analytic)= = 0.33348709214081439678177148703079 y2(numeric) = = 0.33348709214035964824928604787984 absolute error = 4.5474853248543915095e-13 relative error = 1.3636165932725885022461565464042e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.35 y1(analytic)= = 0.93937271284737892003503235730367 y1(numeric) = = 0.93937271284626870759828769594134 absolute error = 1.11021243674466136233e-12 relative error = 1.1818657510067987142205451350307e-10 % glob_h = 0.01 y2(analytic)= = 0.34289780745545134918963490691763 y2(numeric) = = 0.34289780745496652662136988407207 absolute error = 4.8482256826502284556e-13 relative error = 1.4138981286079238041578410307463e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.36 y1(analytic)= = 0.93589682367793485835091236812474 y1(numeric) = = 0.93589682367678533721793803218948 absolute error = 1.14952113297433593526e-12 relative error = 1.2282562606173717091459138385703e-10 % glob_h = 0.01 y2(analytic)= = 0.35227423327508997684991343592073 y2(numeric) = = 0.35227423327457424057257500276266 absolute error = 5.1573627733843315807e-13 relative error = 1.4640193026428252048686138280714e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.37 y1(analytic)= = 0.93232734560603442320381290449088 y1(numeric) = = 0.93232734560484610503936562888766 absolute error = 1.18831816444727560322e-12 relative error = 1.2745718229200294491896808973309e-10 % glob_h = 0.01 y2(analytic)= = 0.36161543196496197803729246912715 y2(numeric) = = 0.36161543196441449539179059419531 absolute error = 5.4748264550187493184e-13 relative error = 1.5139913762168263740780702152357e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.38 y1(analytic)= = 0.92866463557651024949253080772456 y1(numeric) = = 0.92866463557528365866337813766057 absolute error = 1.22659082915267006399e-12 relative error = 1.3208113910692946322781681828508e-10 % glob_h = 0.01 y2(analytic)= = 0.3709204694129826718454854663492 y2(numeric) = = 0.37092046941240261735862162040226 absolute error = 5.8005448686384594694e-13 relative error = 1.5638244170828263480814414962217e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.39 y1(analytic)= = 0.9249090598573130414506767528811 y1(numeric) = = 0.9249090598560487149326075478905 absolute error = 1.26432651806920499060e-12 relative error = 1.3669738712087589829633327712168e-10 % glob_h = 0.01 y2(analytic)= = 0.38018841512316142823118209784716 y2(numeric) = = 0.38018841512254798378621725299365 absolute error = 6.1344444496484485351e-13 relative error = 1.6135274526082561141599914110017e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.4 y1(analytic)= = 0.9210609940028850827985267320518 y1(numeric) = = 0.9210609940015835700812226070409 absolute error = 1.30151271730412501090e-12 relative error = 1.4130581207741907928655980764482e-10 % glob_h = 0.01 y2(analytic)= = 0.38941834230865049166631175679571 y2(numeric) = = 0.38941834230800284667238881896942 absolute error = 6.4764499392293782629e-13 relative error = 1.6631085995677587763417164700283e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.41 y1(analytic)= = 0.91712082281660510547564205827702 y1(numeric) = = 0.91712082281526696846542341747475 absolute error = 1.33813701021864080227e-12 relative error = 1.4590629466999088052375719188333e-10 % glob_h = 0.01 y2(analytic)= = 0.39860932798442289359379764005114 y2(numeric) = = 0.39860932798374024515419261165889 absolute error = 6.8264843960502839225e-13 relative error = 1.7125751749384684695051520331631e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.42 y1(analytic)= = 0.91308894031230827243608878966567 y1(numeric) = = 0.91308894031093408535654940930524 absolute error = 1.37418707953938036043e-12 relative error = 1.5049871035228621190945340052565e-10 % glob_h = 0.01 y2(analytic)= = 0.40776045305957018597278715808634 y2(numeric) = = 0.40776045305885173905196348664945 absolute error = 7.1844692082367143689e-13 relative error = 1.7619337908640019911310367471979e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.43 y1(analytic)= = 0.90896574967488512247591047766345 y1(numeric) = = 0.90896574967347547176645489134343 absolute error = 1.40965070945558632002e-12 relative error = 1.5508292913784529231682010737040e-10 % glob_h = 0.01 y2(analytic)= = 0.41687080242921076621691867262457 y2(numeric) = = 0.41687080242845573380635940365627 absolute error = 7.5503241055926896830e-13 relative error = 1.8111904363642300219034134992553e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=4.1MB, time=0.61 x[1] = = 0.44 y1(analytic)= = 0.90475166321996341716553738899837 y1(numeric) = = 0.90475166321851890137783562593686 absolute error = 1.44451578770176306151e-12 relative error = 1.5965881538817045262244115094022e-10 % glob_h = 0.01 y2(analytic)= = 0.42593946506599960276972075077992 y2(numeric) = = 0.42593946506520720605251326896725 absolute error = 7.9239671720748181267e-13 relative error = 1.8603505478993345110583062918633e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.45 y1(analytic)= = 0.90044710235267692166884061148645 y1(numeric) = = 0.90044710235119815136121513225174 absolute error = 1.47877030762547923471e-12 relative error = 1.6422622758869084912412110403738e-10 % glob_h = 0.01 y2(analytic)= = 0.4349655341112302104208442462319 y2(numeric) = = 0.43496553411039967893499255820221 absolute error = 8.3053148585168802969e-13 relative error = 1.9094190705218104584219451825693e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.46 y1(analytic)= = 0.89605249752552524253638990350041 y1(numeric) = = 0.8960524975240128401661498702381 absolute error = 1.51240237024003326231e-12 relative error = 1.6878501811183785881606381663105e-10 % glob_h = 0.01 y2(analytic)= = 0.4439481069655197652415136439289 y2(numeric) = = 0.44394810696465033704195332845592 absolute error = 8.6942819956031547298e-13 relative error = 1.9584005110485617688467676302228e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.47 y1(analytic)= = 0.89156828819532893645401927653339 y1(numeric) = = 0.89156828819378353626775758517494 absolute error = 1.54540018626169135845e-12 relative error = 1.7333503296643923275728157649720e-10 % glob_h = 0.01 y2(analytic)= = 0.45288628537906829070327480039641 y2(numeric) = = 0.45288628537815921252256592781742 absolute error = 9.0907818070887257899e-13 relative error = 2.0072989844414678709631345458940e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.48 y1(analytic)= = 0.88699492277928419439995483115874 y1(numeric) = = 0.88699492277770644232182362155284 absolute error = 1.57775207813120960590e-12 relative error = 1.7787611153258092531823554083258e-10 % glob_h = 0.01 y2(analytic)= = 0.46177917554148288913664294258864 y2(numeric) = = 0.46177917554053341654431644444034 absolute error = 9.4947259232649814830e-13 relative error = 2.0561182543867321334013845742330e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.49 y1(analytic)= = 0.88233285861012149570546815913666 y1(numeric) = = 0.88233285860851204922344880545503 absolute error = 1.60944648201935368163e-12 relative error = 1.8240808628102148014128596304499e-10 % glob_h = 0.01 y2(analytic)= = 0.47062588817115803618135833718796 y2(numeric) = = 0.4706258881701674337418914896015 absolute error = 9.9060243946684758646e-13 relative error = 2.1048617689016367490212857700543e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.5 y1(analytic)= = 0.87758256189037271611628158260383 y1(numeric) = = 0.87758256188873224416646545069985 absolute error = 1.64047194981613190398e-12 relative error = 1.8693078247617448027086162151716e-10 % glob_h = 0.01 y2(analytic)= = 0.47942553860420300027328793521557 y2(numeric) = = 0.47942553860317054170268480541805 absolute error = 1.03245857060312979752e-12 relative error = 2.1535326916647458275982600534796e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.51 y1(analytic)= = 0.87274450764575126310580847357551 y1(numeric) = = 0.87274450764408044595470501418118 absolute error = 1.67081715110345939433e-12 relative error = 1.9144401786159935474085001393313e-10 % glob_h = 0.01 y2(analytic)= = 0.48817724688290749450013023767457 y2(numeric) = = 0.48817724688183246282108313200123 absolute error = 1.07503167904710567334e-12 relative error = 2.2021339296564123821398486422369e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.52 y1(analytic)= = 0.86781917967764990038784757198851 y1(numeric) = = 0.8678191796759494295127365986855 absolute error = 1.70047087511097330301e-12 relative error = 1.9594760232685921902512629432692e-10 % glob_h = 0.01 y2(analytic)= = 0.49688013784373671433445894254775 y2(numeric) = = 0.49688013784261840203006708665287 absolute error = 1.11831230439185589488e-12 relative error = 2.2506681576061563083255056303936e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.53 y1(analytic)= = 0.8628070705147610118066950185642 y1(numeric) = = 0.86280707051303158977404029732226 absolute error = 1.72942203265472124194e-12 relative error = 2.0044133755451579513198721605609e-10 % glob_h = 0.01 y2(analytic)= = 0.50553334120484696181366102246608 y2(numeric) = = 0.50553334120368467097968289990626 absolute error = 1.16229083397812255982e-12 relative error = 2.2991378396685237790737106122648e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.54 y1(analytic)= = 0.8577086813638241425379687789178 y1(numeric) = = 0.85770868136206648287991033162243 absolute error = 1.75765965805844729537e-12 relative error = 2.0492501664593512616110932653840e-10 % glob_h = 0.01 y2(analytic)= = 0.51413599165311310467728068295824 y2(numeric) = = 0.5141359916519061471728966569852 absolute error = 1.20695750438402597304e-12 relative error = 2.3475452486865744578848446798931e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.55 y1(analytic)= = 0.85252452205950574280498179761777 y1(numeric) = = 0.8525245220577205698939245953731 absolute error = 1.78517291105720224467e-12 relative error = 2.0939842372447301371711500189754e-10 % glob_h = 0.01 y2(analytic)= = 0.52268722893065916778837810775729 y2(numeric) = = 0.52268722892940686538544015297318 absolute error = 1.25230240293795478411e-12 relative error = 2.3958924833499001805438248550979e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.56 y1(analytic)= = 0.84725511101341612609452550386632 y1(numeric) = = 0.84725511101160417501584249692294 absolute error = 1.81195107868300694338e-12 relative error = 2.1386133351449502642283400942642e-10 % glob_h = 0.01 y2(analytic)= = 0.53118619792088340385186944111203 y2(numeric) = = 0.53118619791958508838261501658325 absolute error = 1.29831546925442452878e-12 relative error = 2.4441814835102320337841640585307e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.57 y1(analytic)= = 0.84190097516226874013375636391601 y1(numeric) = = 0.8419009751604307565566240638024 absolute error = 1.83798357713230011361e-12 relative error = 2.1831351089456162346642060973591e-10 % glob_h = 0.01 y2(analytic)= = 0.53963204873396924099446349307883 y2(numeric) = = 0.53963204873262425449767079654825 absolute error = 1.34498649679269653058e-12 relative error = 2.4924140438807690801731080496046e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.58 y1(analytic)= = 0.83646264991518693465788732805002 y1(numeric) = = 0.83646264991332367470427242384457 absolute error = 1.86325995361490420545e-12 relative error = 2.2275471042297337526710490604936e-10 % glob_h = 0.01 y2(analytic)= = 0.54802393679187355618269605957646 y2(numeric) = = 0.54802393679048125104825811353319 absolute error = 1.39230513443794604327e-12 relative error = 2.5405918263141677062768103793015e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.2MB, time=0.82 NO POLE NO POLE x[1] = = 0.59 y1(analytic)= = 0.83094067910016349524799652249068 y1(numeric) = = 0.83094067909827572535981227712525 absolute error = 1.88776988818424536543e-12 relative error = 2.2718467583372329439742259435141e-10 % glob_h = 0.01 y2(analytic)= = 0.55636102291278377572254337887577 y2(numeric) = = 0.55636102291134351483443861340863 absolute error = 1.44026088810476546714e-12 relative error = 2.5887163708276946185873121032009e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.6 y1(analytic)= = 0.82533561490967829724095249895538 y1(numeric) = = 0.82533561490776679404540393295609 absolute error = 1.91150319554856599929e-12 relative error = 2.3160313950074163448411007800868e-10 % glob_h = 0.01 y2(analytic)= = 0.56464247339503535720094544565866 y2(numeric) = = 0.56464247339354651407858266020835 absolute error = 1.48884312236278545031e-12 relative error = 2.6367891055215758169625381051112e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.61 y1(analytic)= = 0.81964801784547951790074657865482 y1(numeric) = = 0.81964801784354506807388370776749 absolute error = 1.93444982686287088733e-12 relative error = 2.3600982186814174689826942943516e-10 % glob_h = 0.01 y2(analytic)= = 0.57286746010048126119097603216272 y2(numeric) = = 0.57286746009894322012889183846985 absolute error = 1.53804106208419369287e-12 relative error = 2.6848113555174183951864814810828e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.62 y1(analytic)= = 0.8138784566625339286839996543607 y1(numeric) = = 0.81387845666057732881249830404335 absolute error = 1.95659987150135031735e-12 relative error = 2.4040443084398211382916324223104e-10 % glob_h = 0.01 y2(analytic)= = 0.58103516053730507584296322758221 y2(numeric) = = 0.58103516053571723204885029927693 absolute error = 1.58784379411292830528e-12 relative error = 2.7327843510272070321680076670616e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.63 y1(analytic)= = 0.80802750831215187252370896577706 y1(numeric) = = 0.80802750831017392896489893953694 absolute error = 1.97794355881002624012e-12 relative error = 2.4478666115484772501543057815312e-10 % glob_h = 0.01 y2(analytic)= = 0.58914475794226951311811209079462 y2(numeric) = = 0.58914475794063127284915677116003 absolute error = 1.63824026895531963459e-12 relative error = 2.7807092346493411939740425557023e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.64 y1(analytic)= = 0.80209575788429261358611077926032 y1(numeric) = = 0.80209575788229414232627140923439 absolute error = 1.99847125983937002593e-12 relative error = 2.4915619365832154740062498402206e-10 % glob_h = 0.01 y2(analytic)= = 0.59719544136239205188354623920793 y2(numeric) = = 0.59719544136070283258105428764524 absolute error = 1.68921930249195156269e-12 relative error = 2.8285870679761168692425954446578e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.65 y1(analytic)= = 0.79608379854905582891760457067991 y1(numeric) = = 0.7960837985470376554285479276736 absolute error = 2.01817348905664300631e-12 relative error = 2.5351269461016172816354957123444e-10 % glob_h = 0.01 y2(analytic)= = 0.60518640573603956037252167860594 y2(numeric) = = 0.60518640573429879079481116820557 absolute error = 1.74076957771051040037e-12 relative error = 2.8764188375866644653153959255415e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.66 y1(analytic)= = 0.78999223149736509278381709123024 y1(numeric) = = 0.7899922314953280518777793776068 absolute error = 2.03704090603771362344e-12 relative error = 2.5785581488271987962120764588100e-10 % glob_h = 0.01 y2(analytic)= = 0.6131168519734337886151454793963 y2(numeric) = = 0.61311685197164090896868609274677 absolute error = 1.79287964645938664953e-12 relative error = 2.9242054604903792628523824519028e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.67 y1(analytic)= = 0.78382166588084928530294214483812 y1(numeric) = = 0.78382166587879422098580403715733 absolute error = 2.05506431713810768079e-12 relative error = 2.6218518913082752263053849333507e-10 % glob_h = 0.01 y2(analytic)= = 0.62098598703655968035744391412659 y2(numeric) = = 0.6209859870347141424262221220423 absolute error = 1.84553793122179208429e-12 relative error = 2.9719477890781110702942353415096e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.68 y1(analytic)= = 0.77757271875092793718239408404432 y1(numeric) = = 0.77757271874885570250525103315445 absolute error = 2.07223467714305088987e-12 relative error = 2.6650043490103837098429725796750e-10 % glob_h = 0.01 y2(analytic)= = 0.62879302401846851370417818742025 y2(numeric) = = 0.62879302401656978097726803560986 absolute error = 1.89873272691015181039e-12 relative error = 3.0196466156316381548905857566892e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.69 y1(analytic)= = 0.77124601499710660197353931549777 y1(numeric) = = 0.77124601499501805888264304985504 absolute error = 2.08854309089626564273e-12 relative error = 2.7080115167974008888828221751155e-10 % glob_h = 0.01 y2(analytic)= = 0.63653718222196794023742920700872 y2(numeric) = = 0.63653718222001548803474867880836 absolute error = 1.95245220268052820036e-12 relative error = 3.0673026764360881328480317012673e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.7 y1(analytic)= = 0.76484218728448842625585999019186 y1(numeric) = = 0.76484218728238444544095270348799 absolute error = 2.10398081490728670387e-12 relative error = 2.7508691987523646556923268265172e-10 % glob_h = 0.01 y2(analytic)= = 0.64421768723769105367261435139872 y2(numeric) = = 0.64421768723568436926884752052674 absolute error = 2.00668440376683087198e-12 relative error = 3.1149166555348596786097604905721e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.71 y1(analytic)= = 0.75836187599050816654145794413955 y1(numeric) = = 0.75836187598838962728252088082814 absolute error = 2.11853925893706331141e-12 relative error = 2.7935729972844513627086709870454e-10 % glob_h = 0.01 y2(analytic)= = 0.65183377102153668121012797285284 y2(numeric) = = 0.6518337710194752639567934086756 absolute error = 2.06141725333456417724e-12 relative error = 3.1624891881621375149095728975137e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.72 y1(analytic)= = 0.75180572914089497944548696225195 y1(numeric) = = 0.75180572913876276945792534424896 absolute error = 2.13220998756161800299e-12 relative error = 2.8361183014635196710509876946881e-10 % glob_h = 0.01 y2(analytic)= = 0.65938467197147315361800383264817 y2(numeric) = = 0.65938467196935651506364997164691 absolute error = 2.11663855435386100126e-12 relative error = 3.2100208638841892480737357747343e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=19.0MB, alloc=4.2MB, time=1.03 x[1] = = 0.73 y1(analytic)= = 0.74517440234487038879013215855033 y1(numeric) = = 0.74517440234272540406841862321195 absolute error = 2.14498472171353533838e-12 relative error = 2.8785002745180527948066270053623e-10 % glob_h = 0.01 y2(analytic)= = 0.66686963500369787373259413076153 y2(numeric) = = 0.6668696350015255377411025817277 absolute error = 2.17233599149154903383e-12 relative error = 3.2575122294772098371565712111467e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.74 y1(analytic)= = 0.73846855872958790979142456069883 y1(numeric) = = 0.73846855872743105445122350412246 absolute error = 2.15685534020105657637e-12 relative error = 2.9207138404261472570841707869865e-10 % glob_h = 0.01 y2(analytic)= = 0.67428791162814506748388115760817 y2(numeric) = = 0.67428791162591657035085916453652 absolute error = 2.22849713302199307165e-12 relative error = 3.3049637915664728086229833020951e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.75 y1(analytic)= = 0.73168886887382088631183875300008 y1(numeric) = = 0.73168886887165307243063419372129 absolute error = 2.16781388120455927879e-12 relative error = 2.9627536695223347874746412152194e-10 % glob_h = 0.01 y2(analytic)= = 0.68163876002333416673324195277989 y2(numeric) = = 0.68163876002104905730048549844252 absolute error = 2.28510943275645433737e-12 relative error = 3.3523760190489012631690589853601e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.76 y1(analytic)= = 0.72483601074090517233968836666701 y1(numeric) = = 0.72483601073872731979593816290809 absolute error = 2.17785254375020375892e-12 relative error = 3.0046141630354010483584937600864e-10 % glob_h = 0.01 y2(analytic)= = 0.68892144511055133914775563876973 y2(numeric) = = 0.68892144510820917891576493350778 absolute error = 2.34216023199070526195e-12 relative error = 3.3997493453188388105095158583697e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.77 y1(analytic)= = 0.71791066961094336337129056532434 y1(numeric) = = 0.71791066960875639968213003406019 absolute error = 2.18696368916053126415e-12 relative error = 3.0462894364638853835369320980646e-10 % glob_h = 0.01 y2(analytic)= = 0.69613523862735674701988373445221 y2(numeric) = = 0.6961352386249571102584130987819 absolute error = 2.39963676147063567031e-12 relative error = 3.4470841703147401346139150001215e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.78 y1(analytic)= = 0.71091353801227735721626502376456 y1(numeric) = = 0.7109135380100822173737832219802 absolute error = 2.19513984248180178436e-12 relative error = 3.0877733016865014160587679701286e-10 % glob_h = 0.01 y2(analytic)= = 0.70327941920041018436789732511792 y2(numeric) = = 0.70327941919795265822452174128044 absolute error = 2.45752614337558383748e-12 relative error = 3.4943808624026779953221228113936e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.79 y1(analytic)= = 0.70384531565223609691278086108495 y1(numeric) = = 0.70384531565003372321889299867889 absolute error = 2.20237369388786240606e-12 relative error = 3.1290592476941854977540087121969e-10 % glob_h = 0.01 y2(analytic)= = 0.7103532724176078098140288749692 y2(numeric) = = 0.7103532724150919944207097515267 absolute error = 2.51581539331912344250e-12 relative error = 3.5416397601109480342194923613267e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.8 y1(analytic)= = 0.69670670934716542092074998164232 y1(numeric) = = 0.69670670934495676282068964145288 absolute error = 2.20865810006034018944e-12 relative error = 3.1701404198187175146260172970745e-10 % glob_h = 0.01 y2(analytic)= = 0.71735609089952276162717461058139 y2(numeric) = = 0.71735609089694827020480757553917 absolute error = 2.57449142236703504222e-12 relative error = 3.5888611737286188343798538217165e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.81 y1(analytic)= = 0.6894984329517470175496392406801 y1(numeric) = = 0.68949843294953303146409428405106 absolute error = 2.21398608554495662904e-12 relative error = 3.2110095973197047407755423884108e-10 % glob_h = 0.01 y2(analytic)= = 0.72428717437014251092817685251454 y2(numeric) = = 0.72428717436750896988910466419878 absolute error = 2.63354103907218831576e-12 relative error = 3.6360453867795998641397796266796e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.82 y1(analytic)= = 0.68222120728761355166655797843693 y1(numeric) = = 0.68222120728539520082247421456755 absolute error = 2.21835084408376386938e-12 relative error = 3.2516591691769889922578690610482e-10 % glob_h = 0.01 y2(analytic)= = 0.73114582972689587938131336468772 y2(numeric) = = 0.73114582972420292842978730569401 absolute error = 2.69295095152605899371e-12 relative error = 3.6831926573826648036462113814665e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.83 y1(analytic)= = 0.67487576007126710211246291786445 y1(numeric) = = 0.6748757600690453563725398118805 absolute error = 2.22174573992310598395e-12 relative error = 3.2920811079190174254731349814016e-10 % glob_h = 0.01 y2(analytic)= = 0.73793137110996271872858022613808 y2(numeric) = = 0.73793137110721001095915362405376 absolute error = 2.75270776942660208432e-12 relative error = 3.7303032195068554696545763057032e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.84 y1(analytic)= = 0.66746282584130811792267103687086 y1(numeric) = = 0.66746282583908395361357392508195 absolute error = 2.22416430909711178891e-12 relative error = 3.3322669412991630808946781131632e-10 % glob_h = 0.01 y2(analytic)= = 0.74464311997085932125657267062965 y2(numeric) = = 0.74464311996804652325041046988718 absolute error = 2.81279800616220074247e-12 relative error = 3.7773772841307874843449507655873e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.85 y1(analytic)= = 0.65998314588498217039541602946147 y1(numeric) = = 0.65998314588275657013472950060999 absolute error = 2.22560026068652885148e-12 relative error = 3.3722077216111104518955837703598e-10 % glob_h = 0.01 y2(analytic)= = 0.75128040514029270271207152423547 y2(numeric) = = 0.75128040513741949463116011633966 absolute error = 2.87320808091140789581e-12 relative error = 3.8244150403135702354857947577267e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.86 y1(analytic)= = 0.65243746816405184627203066422386 y1(numeric) = = 0.6524374681618257987939779526569 absolute error = 2.22604747805271156696e-12 relative error = 3.4118939924109080415665839047549e-10 % glob_h = 0.01 y2(analytic)= = 0.75784256289527697229458872952865 y2(numeric) = = 0.75784256289234304797383053398145 absolute error = 2.93392432075819554720e-12 relative error = 3.8714166561843294369635216576863e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.87 y1(analytic)= = 0.64482654724000119477766380548283 y1(numeric) = = 0.64482654723777569475761722606593 absolute error = 2.22550002004657941690e-12 relative error = 3.4513157523867569812881891675267e-10 % glob_h = 0.01 y2(analytic)= = 0.76432893702550507814480282372285 y2(numeric) = = 0.76432893702251014518198039920994 absolute error = 2.99493296282242451291e-12 relative error = 3.9183822798566710116079838522191e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=1.23 NO POLE NO POLE x[1] = = 0.88 y1(analytic)= = 0.63715114419858020801549860572209 y1(numeric) = = 0.63715114419635625589330624093792 absolute error = 2.22395212219236478417e-12 relative error = 3.4904624160876152040826305504908e-10 % glob_h = 0.01 y2(analytic)= = 0.77073887889896929120964513075599 y2(numeric) = = 0.77073887889591307105323988552269 absolute error = 3.05622015640524523330e-12 relative error = 3.9653120402738415889667276129656e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.89 y1(analytic)= = 0.62941202657369688020355305738025 y1(numeric) = = 0.62941202657147548200570708439235 absolute error = 2.22139819784597298790e-12 relative error = 3.5293227711877426454483310261796e-10 % glob_h = 0.01 y2(analytic)= = 0.77707174752682386549033371297318 y2(numeric) = = 0.77707174752370609352518457476751 absolute error = 3.11777196514913820567e-12 relative error = 4.0122060479898161917400268890533e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.9 y1(analytic)= = 0.62160996827066445648471615140713 y1(numeric) = = 0.62160996826844662364538837089524 absolute error = 2.21783283932778051189e-12 relative error = 3.5678849319258034742298307504266e-10 % glob_h = 0.01 y2(analytic)= = 0.78332690962748338846138231571355 y2(numeric) = = 0.78332690962430381409217001517395 absolute error = 3.17957436921230053960e-12 relative error = 4.0590643958910711421549248350473e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.91 y1(analytic)= = 0.61374574948881154652117822617468 y1(numeric) = = 0.61374574948659829570214852544029 absolute error = 2.21325081902970073439e-12 relative error = 3.6061362883133870444671574127845e-10 % glob_h = 0.01 y2(analytic)= = 0.78950373968995041187895751787155 y2(numeric) = = 0.7895037396867087986115004347492 absolute error = 3.24161326745708312235e-12 relative error = 4.1058871598633741052792429467160e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.92 y1(analytic)= = 0.60582015664346284179740470667438 y1(numeric) = = 0.60582015664125519470690835685069 absolute error = 2.20764709049634982369e-12 relative error = 3.6440634506580041883577474741442e-10 % glob_h = 0.01 y2(analytic)= = 0.79560162003636603026827610248162 y2(numeric) = = 0.79560162003306215578862392157507 absolute error = 3.30387447965218090655e-12 relative error = 4.1526743994075384407171646685316e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.93 y1(analytic)= = 0.59783398228729823849490708443298 y1(numeric) = = 0.59783398228509722170542693558951 absolute error = 2.20101678948014884347e-12 relative error = 3.6816521888888153816109510018730e-10 % glob_h = 0.01 y2(analytic)= = 0.80161994088377715208431921591065 y2(numeric) = = 0.80161994088041080833563093901579 absolute error = 3.36634374868827689486e-12 relative error = 4.1994261582077411951239246135588e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.94 y1(analytic)= = 0.58978802503109822996098981522402 y1(numeric) = = 0.58978802502890487472601961371106 absolute error = 2.19335523497020151296e-12 relative error = 3.7188873661084432808715299182659e-10 % glob_h = 0.01 y2(analytic)= = 0.80755810040511428687021979863415 y2(numeric) = = 0.80755810040168528012741296013767 absolute error = 3.42900674280683849648e-12 relative error = 4.2461424646556891943275078234464e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.95 y1(analytic)= = 0.58168308946388349416618097376046 y1(numeric) = = 0.5816830894616988362359861832709 absolute error = 2.18465793019479048956e-12 relative error = 3.7557528657199087439607535815114e-10 % glob_h = 0.01 y2(analytic)= = 0.81341550478937375068542210210256 y2(numeric) = = 0.81341550478588190162758033903403 absolute error = 3.49184905784176306853e-12 relative error = 4.2928233323336323002467732993076e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.96 y1(analytic)= = 0.57351998607245666212505080035186 y1(numeric) = = 0.5735199860702817415614534618659 absolute error = 2.17492056359733848596e-12 relative error = 3.7922315113924661879857580803671e-10 % glob_h = 0.01 y2(analytic)= = 0.81919156830099827163322214643043 y2(numeric) = = 0.81919156829744341541374857879809 absolute error = 3.55485621947356763234e-12 relative error = 4.3394687604589638984607944319640e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.97 y1(analytic)= = 0.56529953116035431303652775484986 y1(numeric) = = 0.56529953115819017402674207085198 absolute error = 2.16413900978568399788e-12 relative error = 3.8283049790320784520038674313038e-10 % glob_h = 0.01 y2(analytic)= = 0.82488571333845005747662003785634 y2(numeric) = = 0.8248857133348320437911242218868 absolute error = 3.61801368549581596954e-12 relative error = 4.3860787342929133381918358108517e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.98 y1(analytic)= = 0.55702254676621730087665826735994 y1(numeric) = = 0.55702254676406499154620374245611 absolute error = 2.15230933045452490383e-12 relative error = 3.8639536998093013083347252536658e-10 % glob_h = 0.01 y2(analytic)= = 0.83049737049197046808453328771915 y2(numeric) = = 0.83049737048828916123643981316197 absolute error = 3.68130684809347455718e-12 relative error = 4.4326532255156209284162617878787e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 0.99 y1(analytic)= = 0.54868986058158757534312640865361 y1(numeric) = = 0.54868986057944814756784552195073 absolute error = 2.13942777528088670288e-12 relative error = 3.8991567531668720484881963400834e-10 % glob_h = 0.01 y2(analytic)= = 0.83602597860052051678925941154711 y2(numeric) = = 0.83602597859677579575312652445303 absolute error = 3.74472103613288709408e-12 relative error = 4.4791921925696910387151069812286e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1 y1(analytic)= = 0.54030230586813971740093660744298 y1(numeric) = = 0.54030230586601422661814413176217 absolute error = 2.12549078279247568081e-12 relative error = 3.9338917485782482640221258874570e-10 % glob_h = 0.01 y2(analytic)= = 0.8414709848078965066525023216303 y2(numeric) = = 0.84147098480408826513503926592716 absolute error = 3.80824151746305570314e-12 relative error = 4.5256955809741409373401811639814e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.01 y1(analytic)= = 0.53186072137435546620673135577918 y1(numeric) = = 0.53186072137224497122552257494137 absolute error = 2.11049498120878083781e-12 relative error = 3.9681346946530535843462870644457e-10 % glob_h = 0.01 y2(analytic)= = 0.84683184461801519012309878478201 y2(numeric) = = 0.84683184461414333662187086951609 absolute error = 3.87185350122791526592e-12 relative error = 4.5721633236105005047554603952720e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=1.43 NO POLE NO POLE x[1] = = 1.02 y1(analytic)= = 0.52336595125164956988961380803381 y1(numeric) = = 0.52336595124955513270035901606059 absolute error = 2.09443718925479197322e-12 relative error = 4.0018598539814556300913315867903e-10 % glob_h = 0.01 y2(analytic)= = 0.85210802194936292361654998545538 y2(numeric) = = 0.85210802194542738147636069969766 absolute error = 3.93554214018928575772e-12 relative error = 4.6185953409826693578359315030966e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.03 y1(analytic)= = 0.51481884496995534753350229983735 y1(numeric) = = 0.5148188449678780331165550949354 absolute error = 2.07731441694720490195e-12 relative error = 4.0350395818716314937459124323823e-10 % glob_h = 0.01 y2(analytic)= = 0.85729898918860337214627438529442 y2(numeric) = = 0.85729898918460407961321419939188 absolute error = 3.99929253306018590254e-12 relative error = 4.6649915414520018368857611090494e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.04 y1(analytic)= = 0.50622025723277840373447342099217 y1(numeric) = = 0.50622025723071927986812043261685 absolute error = 2.05912386635298837532e-12 relative error = 4.0676441468562737975436700134992e-10 % glob_h = 0.01 y2(analytic)= = 0.86240422724333840328079169211617 y2(numeric) = = 0.86240422723927531355394350215713 absolute error = 4.06308972684818995904e-12 relative error = 4.7113518214489655203354646059501e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.05 y1(analytic)= = 0.4975710478917269902908495728121 y1(numeric) = = 0.49757104788968712735852938191874 absolute error = 2.03986293232019089336e-12 relative error = 4.0996415305178114394585741960790e-10 % glob_h = 0.01 y2(analytic)= = 0.86742322559401689438140948500027 y2(numeric) = = 0.86742322558988997566220097701992 absolute error = 4.12691871920850798035e-12 relative error = 4.7576760656626043409805368531807e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.06 y1(analytic)= = 0.48887208186052756191863753995641 y1(numeric) = = 0.48887208185850803271545667072899 absolute error = 2.01952920318086922742e-12 relative error = 4.1309972037982514189489615413792e-10 % glob_h = 0.01 y2(analytic)= = 0.87235548234498626228294592199742 y2(numeric) = = 0.87235548234079549782213945353423 absolute error = 4.19076446080646846319e-12 relative error = 4.8039641472089319980946835525137e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.07 y1(analytic)= = 0.48012422902853412436509306817592 y1(numeric) = = 0.48012422902653600390366704405635 absolute error = 1.99812046142602411957e-12 relative error = 4.1616738765068121559239112066905e-10 % glob_h = 0.01 y2(analytic)= = 0.87720050427468161030706325777682 y2(numeric) = = 0.87720050427042699844937417686233 absolute error = 4.25461185768908091449e-12 relative error = 4.8502159277792843050060757360763e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.08 y1(analytic)= = 0.47132836417374002391352478852603 y1(numeric) = = 0.47132836417176438922917235623696 absolute error = 1.97563468435243228907e-12 relative error = 4.1916312162027621603741528893694e-10 % glob_h = 0.01 y2(analytic)= = 0.88195780688494747373533498762476 y2(numeric) = = 0.88195780688062902796166963310685 absolute error = 4.31844577366535451791e-12 relative error = 4.8964312577695695864480965428834e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.09 y1(analytic)= = 0.46248536687530087702789707387514 y1(numeric) = = 0.46248536687334880698321580631981 absolute error = 1.95207004468126755533e-12 relative error = 4.2208255319948334654834938637025e-10 % glob_h = 0.01 y2(analytic)= = 0.88662691444948723160860062863605 y2(numeric) = = 0.88662691444510498057590558085865 absolute error = 4.38225103269504777740e-12 relative error = 4.9426099763912735252145025137971e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.1 y1(analytic)= = 0.45359612142557738777137005178472 y1(numeric) = = 0.45359612142364996286022164420395 absolute error = 1.92742491114840758077e-12 relative error = 4.2492094180409451441200287903624e-10 % glob_h = 0.01 y2(analytic)= = 0.8912073600614353399518025778717 y2(numeric) = = 0.89120736005698932753051705512034 absolute error = 4.44601242128552275136e-12 relative error = 4.9887519117649983071566109044309e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.11 y1(analytic)= = 0.44466151674170684864373751193357 y1(numeric) = = 0.44466151673980515079467118548774 absolute error = 1.90169784906632644583e-12 relative error = 4.2767313506263616329258547498721e-10 % glob_h = 0.01 y2(analytic)= = 0.89569868568004762924062595933937 y2(numeric) = = 0.89569868567553791454972958307106 absolute error = 4.50971469089637626831e-12 relative error = 5.0348568809972449416088750368102e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.12 y1(analytic)= = 0.43568244627671216761398879396113 y1(numeric) = = 0.43568244627483727999313131697023 absolute error = 1.87488762085747699090e-12 relative error = 4.3033352316119979068217899858559e-10 % glob_h = 0.01 y2(analytic)= = 0.90010044217650499711910324733915 y2(numeric) = = 0.90010044217193165455875172800484 absolute error = 4.57334256035151933431e-12 relative error = 5.0809246902410817130746585200140e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.13 y1(analytic)= = 0.42665980793015731037121583565354 y1(numeric) = = 0.4266598079283103171846567650575 absolute error = 1.84699318655907059604e-12 relative error = 4.3289598697363516289714777469699e-10 % glob_h = 0.01 y2(analytic)= = 0.9044121893788259160370815224114 y2(numeric) = = 0.90441218937418903531882314760836 absolute error = 4.63688071825837480304e-12 relative error = 5.1269551347412803694982219432260e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.14 y1(analytic)= = 0.41759450395835809217518674082258 y1(numeric) = = 0.41759450395654007847088757500332 absolute error = 1.81801370429916581926e-12 relative error = 4.3535383896730007337322357219175e-10 % glob_h = 0.01 y2(analytic)= = 0.9086334961158832645942155781022 y2(numeric) = = 0.90863349611118295076878171581982 absolute error = 4.70031382543386228238e-12 relative error = 5.1729479988644444389880533297284e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.15 y1(analytic)= = 0.40848744088415729815257671880992 y1(numeric) = = 0.40848744088236934962183273773434 absolute error = 1.78794853074398107558e-12 relative error = 4.3769975568258028734407813108732e-10 % glob_h = 0.01 y2(analytic)= = 0.91276394026052108094403304975368 y2(numeric) = = 0.91276394025575745442669621155785 absolute error = 4.76362651733683819583e-12 relative error = 5.2189030561146005946607692246011e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=4.3MB, time=1.63 x[1] = = 1.16 y1(analytic)= = 0.39933952940627315445163962339401 y1(numeric) = = 0.39933952940451635723012327308015 absolute error = 1.75679722151635031386e-12 relative error = 4.3992570035035281814116472785598e-10 % glob_h = 0.01 y2(analytic)= = 0.91680310877176692661866166687433 y2(numeric) = = 0.91680310876694012321215500897031 absolute error = 4.82680340650665790402e-12 relative error = 5.2648200691346738977936393362697e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.17 y1(analytic)= = 0.3901516843082302153326619350505 y1(numeric) = = 0.39015168430650565580107669061641 absolute error = 1.72455953158524443409e-12 relative error = 4.4202283392497070479478646700501e-10 % glob_h = 0.01 y2(analytic)= = 0.92075059773613563957301300896203 y2(numeric) = = 0.92075059773124581048800548314096 absolute error = 4.88982908500752582107e-12 relative error = 5.3106987896942207151659535943375e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.18 y1(analytic)= = 0.38092482436688177302959946671276 y1(numeric) = = 0.38092482436519053761397318172748 absolute error = 1.69123541562628498528e-12 relative error = 4.4398141245774995943376689531038e-10 % glob_h = 0.01 y2(analytic)= = 0.92460601240802034610753802587476 y2(numeric) = = 0.92460601240306765798065972734326 absolute error = 4.95268812687829853150e-12 relative error = 5.3565389586637488267245940002895e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.19 y1(analytic)= = 0.37165987226053293806567955835047 y1(numeric) = = 0.3716598722588761130373263778585 absolute error = 1.65682502835318049197e-12 relative error = 4.4579066830000656251244818444819e-10 % glob_h = 0.01 y2(analytic)= = 0.92836896724916669260202111160267 y2(numeric) = = 0.92836896724415132751143370657432 absolute error = 5.01536509058740502835e-12 relative error = 5.4023403059759124434405950457915e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.2 y1(analytic)= = 0.36235775447667357763837335562308 y1(numeric) = = 0.36235775447505224891355333604711 absolute error = 1.62132872482001957597e-12 relative error = 4.4743867208294862375556592139072e-10 % glob_h = 0.01 y2(analytic)= = 0.93203908596722634967013443549483 y2(numeric) = = 0.93203908596214850514864188814558 absolute error = 5.07784452149254734925e-12 relative error = 5.4481025505738302880612835547408e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.21 y1(analytic)= = 0.35301940121933033870301071366479 y1(numeric) = = 0.35301940121774559164231635479665 absolute error = 1.58474706069435886814e-12 relative error = 4.4891217174484930967660353862083e-10 % glob_h = 0.01 y2(analytic)= = 0.93561600155338593341646488854361 y2(numeric) = = 0.93561600154824582246216004445625 absolute error = 5.14011095430484408736e-12 relative error = 5.4938254003467373257995796701034e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.22 y1(analytic)= = 0.3436457463160470204755229744352 y1(numeric) = = 0.34364574631449993968302192689273 absolute error = 1.54708079250104754247e-12 relative error = 4.5019640402538701039523910735590e-10 % glob_h = 0.01 y2(analytic)= = 0.93909935631906758093524527188837 y2(numeric) = = 0.93909935631386543201968819339199 absolute error = 5.20214891555707849638e-12 relative error = 5.5395085520531449529673618757913e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.23 y1(analytic)= = 0.33423772712450259823954724549766 y1(numeric) = = 0.33423772712299426736171051134622 absolute error = 1.50833087783673415144e-12 relative error = 4.5127487277188347132243211351269e-10 % glob_h = 0.01 y2(analytic)= = 0.94248880193169751002382356538924 y2(numeric) = = 0.94248880192643356709774785319482 absolute error = 5.26394292607571219442e-12 relative error = 5.5851516912316502640269827347162e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.24 y1(analytic)= = 0.32479628443877623657769341569738 y1(numeric) = = 0.32479628443730773810213841040078 absolute error = 1.46849847555500529660e-12 relative error = 4.5212908703449646118394397634578e-10 % glob_h = 0.01 y2(analytic)= = 0.94578399944953898628470596308179 y2(numeric) = = 0.94578399944421350878124963828159 absolute error = 5.32547750345632480020e-12 relative error = 5.6307544920995022393094381074275e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.25 y1(analytic)= = 0.31532236239526866544753855243804 y1(numeric) = = 0.31532236239384108050161644290706 absolute error = 1.42758494592210953098e-12 relative error = 4.5273825017604590046125717156983e-10 % glob_h = 0.01 y2(analytic)= = 0.94898461935558621434849084703605 y2(numeric) = = 0.94898461935019947718394870782914 absolute error = 5.38673716454213920691e-12 relative error = 5.6763166174390011577958302149275e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.26 y1(analytic)= = 0.30581690837828932688634248917648 y1(numeric) = = 0.30581690837690373503559926541583 absolute error = 1.38559185074322376065e-12 relative error = 4.5307888896361305220096892000742e-10 % glob_h = 0.01 y2(analytic)= = 0.95209034159051576385681622142542 y2(numeric) = = 0.95209034158506805742891092981103 absolute error = 5.44770642790529161439e-12 relative error = 5.7218377184717770846515666808352e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.27 y1(analytic)= = 0.29628087292531873355113701608796 y1(numeric) = = 0.29628087292397621259767779279818 absolute error = 1.34252095345922328978e-12 relative error = 4.5312440867474504058425032391199e-10 % glob_h = 0.01 y2(analytic)= = 0.95510085558469223509018174218289 y2(numeric) = = 0.95510085557918386527385123728431 absolute error = 5.50836981633050489858e-12 relative error = 5.7673174347209637637675723383410e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.28 y1(analytic)= = 0.28671520963195551277938689359259 y1(numeric) = = 0.28671520963065713856017297305501 absolute error = 1.29837421921392053758e-12 relative error = 4.5284455640863627818022819815323e-10 % glob_h = 0.01 y2(analytic)= = 0.95801586028922496370075385916029 y2(numeric) = = 0.9580158602836562518414530357608 absolute error = 5.56871185930082339949e-12 relative error = 5.8127553938612555242030305941655e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.29 y1(analytic)= = 0.27712087505655764138660609006118 y1(numeric) = = 0.27712087505530448757171434871567 absolute error = 1.25315381489174134551e-12 relative error = 4.5220476971862368488819650518231e-10 % glob_h = 0.01 y2(analytic)= = 0.96083506420607265890556129128537 y2(numeric) = = 0.96083506420044394181007622453087 absolute error = 5.62871709548506675450e-12 relative error = 5.8581512115568067549870906234175e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=34.3MB, alloc=4.3MB, time=1.83 x[1] = = 1.3 y1(analytic)= = 0.26749882862458740699798410929287 y1(numeric) = = 0.26749882862338054488885829760462 absolute error = 1.20686210912581168825e-12 relative error = 4.5116538092192670626473185590495e-10 % glob_h = 0.01 y2(analytic)= = 0.96355818541719296470134863003955 y2(numeric) = = 0.96355818541150459462612197004669 absolute error = 5.68837007522665999286e-12 relative error = 5.9035044912869059920987425656818e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.31 y1(analytic)= = 0.2578500325326696613381769786162 y1(numeric) = = 0.25785003253151015966590054711346 absolute error = 1.15950167227643150274e-12 relative error = 4.4968063834916226395588152420902e-10 % glob_h = 0.01 y2(analytic)= = 0.9661849516127340291692578059375 y2(numeric) = = 0.96618495160698637380622430919723 absolute error = 5.74765536303349674027e-12 relative error = 5.9488148241593295777601529883635e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.32 y1(analytic)= = 0.24817545165237295957398272942735 y1(numeric) = = 0.24817545165126188429760281317282 absolute error = 1.11107527637991625453e-12 relative error = 4.4769749343953397978915126775250e-10 % glob_h = 0.01 y2(analytic)= = 0.96871510011826526273589984597277 y2(numeric) = = 0.96871510011245870519583135391368 absolute error = 5.80655754006849205909e-12 relative error = 5.9940817887112530830660027357085e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.33 y1(analytic)= = 0.23847605343372320751578498601058 y1(numeric) = = 0.23847605343266162162071719524065 absolute error = 1.06158589506779076993e-12 relative error = 4.4515408561255171034874398442843e-10 % glob_h = 0.01 y2(analytic)= = 0.9711483779210445623376830377638 y2(numeric) = = 0.97114837791517950113104255659363 absolute error = 5.86506120664048117017e-12 relative error = 6.0393049506975721229372473613600e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.34 y1(analytic)= = 0.22875280780845946523263949230014 y1(numeric) = = 0.2287528078074484285291831685252 absolute error = 1.01103670345632377494e-12 relative error = 4.4197783325260447963778942305887e-10 % glob_h = 0.01 y2(analytic)= = 0.97348454169531937478787034808955 y2(numeric) = = 0.97348454168939622380317522802332 absolute error = 5.92315098469512006623e-12 relative error = 6.0844838628664577332972854515051e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.35 y1(analytic)= = 0.21900668709304158142002217301063 y1(numeric) = = 0.21900668709208215034201577751224 absolute error = 9.5943107800639549839e-13 relative error = 4.3808300593068016308548864131786e-10 % glob_h = 0.01 y2(analytic)= = 0.97572335782665906926111353926522 y2(numeric) = = 0.97572335782067825774080809542964 absolute error = 5.98081152030544383558e-12 relative error = 6.1296180647219450249061209207256e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.36 y1(analytic)= = 0.20923866589141935767597525239186 y1(numeric) = = 0.20923866589051258507962155777736 absolute error = 9.0677259635369461450e-13 relative error = 4.3336760559553937525097912221286e-10 % glob_h = 0.01 y2(analytic)= = 0.97786460243531618567849243942663 y2(numeric) = = 0.97786460242927815819233070106039 absolute error = 6.03802748616173836624e-12 relative error = 6.1747070822733272755309348769769e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.37 y1(analytic)= = 0.19944972099757296568819838964531 y1(numeric) = = 0.19944972099671990065108914492373 absolute error = 8.5306503710924472158e-13 relative error = 4.2770931583284860720864841584277e-10 % glob_h = 0.01 y2(analytic)= = 0.97990806139861422288768850489193 y2(numeric) = = 0.97990806139251943930362812389463 absolute error = 6.09478358406038099730e-12 relative error = 6.2197504277711008787983166423663e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.38 y1(analytic)= = 0.1896408312978343632091500735982 y1(numeric) = = 0.18964083129703605082951980912313 absolute error = 7.9831237963026447507e-13 relative error = 4.2096017728191689462608059447746e-10 % glob_h = 0.01 y2(analytic)= = 0.98185353037235972787813108520605 y2(numeric) = = 0.98185353036620866333073977958217 absolute error = 6.15106454739130562388e-12 relative error = 6.2647475994291795361079729927458e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.39 y1(analytic)= = 0.17981297767299947659616321780405 y1(numeric) = = 0.17981297767225695779240184838671 absolute error = 7.4251880376136941734e-13 relative error = 4.1293949600883854480740969700423e-10 % glob_h = 0.01 y2(analytic)= = 0.98370081481127654484003822444291 y2(numeric) = = 0.98370081480506968969641447669656 absolute error = 6.20685514362374774635e-12 relative error = 6.3096980811330686650265848783538e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.4 y1(analytic)= = 0.16996714290024093861674803520365 y1(numeric) = = 0.16996714289955524992720190773332 absolute error = 6.8568868954612747033e-13 relative error = 4.0342426062228964225110279644462e-10 % glob_h = 0.01 y2(analytic)= = 0.9854497299884601806594745788061 y2(numeric) = = 0.98544972998219804048268465382351 absolute error = 6.26214017678992498259e-12 relative error = 6.3546013421336631083751809893205e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.41 y1(analytic)= = 0.16010431155483119016356254936092 y1(numeric) = = 0.16010431155420336354665356537907 absolute error = 6.2782661690898398185e-13 relative error = 3.9213598360464587175091793920104e-10 % glob_h = 0.01 y2(analytic)= = 0.98710010101385034142908886194224 y2(numeric) = = 0.9871001010075334369391225533083 absolute error = 6.31690448996630863394e-12 relative error = 6.3994568367263027681430900105567e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.42 y1(analytic)= = 0.15022546991168577348698210297591 y1(numeric) = = 0.1502254699111168361216745268357 absolute error = 5.6893736530757614021e-13 relative error = 3.7872230697100952071822728688577e-10 % glob_h = 0.01 y2(analytic)= = 0.9886517628517197927362734733357 y2(numeric) = = 0.98865176284534865976852133132374 absolute error = 6.37113296775214201196e-12 relative error = 6.4442640039146916628951003577743e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.43 y1(analytic)= = 0.14033160584673666253389762457492 y1(numeric) = = 0.1403316058462276366205421640796 absolute error = 5.0902591335546049532e-13 relative error = 3.6273076922628091226481362929208e-10 % glob_h = 0.01 y2(analytic)= = 0.99010456033717779485729149548183 y2(numeric) = = 0.99010456033075298431854663408881 absolute error = 6.42481053874486139302e-12 relative error = 6.4890222670592560186098906410670e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.44 y1(analytic)= = 0.13042370873814549297752015612917 y1(numeric) = = 0.13042370873769739553910487488298 absolute error = 4.4809743841528124619e-13 relative error = 3.4357053847850331107924884028669e-10 % glob_h = 0.01 y2(analytic)= = 0.99145834819168646252760446395798 y2(numeric) = = 0.99145834818520854034959238828564 absolute error = 6.47792217801207567234e-12 relative error = 6.5337310335094862536976061419079e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=2.02 NO POLE NO POLE x[1] = = 1.45 y1(analytic)= = 0.12050276936736657053286662724802 y1(numeric) = = 0.12050276936698041321670421637264 absolute error = 3.8615731616241087538e-13 relative error = 3.2045513824264554777296137227535e-10 % glob_h = 0.01 y2(analytic)= = 0.99271299103758849766535413432301 y2(numeric) = = 0.99271299103105804475579437328604 absolute error = 6.53045290955976103697e-12 relative error = 6.5783896942197760070483758300906e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.46 y1(analytic)= = 0.11056977982006955117464810912337 y1(numeric) = = 0.11056977981974634005452901049476 absolute error = 3.2321112011909862861e-13 relative error = 2.9231415730867946362518956484500e-10 % glob_h = 0.01 y2(analytic)= = 0.99386836341164484228683230125003 y2(numeric) = = 0.99386836340506245447803597398019 absolute error = 6.58238780879632726984e-12 relative error = 6.6229976233482385812805565365924e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.47 y1(analytic)= = 0.10062573338693170090697460146241 y1(numeric) = = 0.10062573338667243628581543520901 absolute error = 2.5926462115916625340e-13 relative error = 2.5765240404482561533404742483579e-10 % glob_h = 0.01 y2(analytic)= = 0.99492434977758089785992846273557 y2(numeric) = = 0.99492434977094718585493625010239 absolute error = 6.63371200499221263318e-12 relative error = 6.6675541778379472237110279655984e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.48 y1(analytic)= = 0.090671624464309655776226540647838 y1(numeric) = = 0.090671624464115331989243246325649 absolute error = 1.94323786983294322189e-13 relative error = 2.1431598709228424126096267462922e-10 % glob_h = 0.01 y2(analytic)= = 0.99588084453764005648407513256269 y2(numeric) = = 0.99588084453095564580034046790294 absolute error = 6.68441068373466465975e-12 relative error = 6.7120586969800104346431624459770e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.49 y1(analytic)= = 0.080708448454800614868318484563714 y1(numeric) = = 0.080708448454672220086753538189345 absolute error = 1.28394781564946374369e-13 relative error = 1.5908468570902050501955229973405e-10 % glob_h = 0.01 y2(analytic)= = 0.9967377520431433885532007170437 y2(numeric) = = 0.99673775203640891946382335243893 absolute error = 6.73446908937736460477e-12 relative error = 6.7565105019578568615511324260318e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.5 y1(analytic)= = 0.070737201667702910088189851434269 y1(numeric) = = 0.070737201667641426123622869419146 absolute error = 6.1483964566982015123e-14 relative error = 8.6918853329554702095546240862007e-11 % glob_h = 0.01 y2(analytic)= = 0.99749498660405443094172337114149 y2(numeric) = = 0.9974949865972705584142388173622 absolute error = 6.78387252748455377929e-12 relative error = 6.8009088953720661876184328703382e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.51 y1(analytic)= = 0.060758881219385906581595514916193 y1(numeric) = = 0.060758881219392308690866500907172 absolute error = 6.402109270985990979e-15 relative error = 1.0536911053166850026934436598366e-11 % glob_h = 0.01 y2(analytic)= = 0.99815247249754811924273786483671 y2(numeric) = = 0.99815247249071551287546854433888 absolute error = 6.83260636726932049783e-12 relative error = 6.8452531607450426290793149133440e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.52 y1(analytic)= = 0.050774484933579196726129270152727 y1(numeric) = = 0.050774484933654453416903701852477 absolute error = 7.5256690774431699750e-14 relative error = 1.4821753656955649699301239196443e-10 % glob_h = 0.01 y2(analytic)= = 0.99871014397558300717231239411685 y2(numeric) = = 0.99871014396870235112828668718786 absolute error = 6.88065604402570692899e-12 relative error = 6.8895425620047860856738422740917e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.53 y1(analytic)= = 0.040785011241591058688989007076121 y1(numeric) = = 0.040785011241736131525993897296008 absolute error = 1.45072837004890219887e-13 relative error = 3.5570135348387561850661707635911e-10 % glob_h = 0.01 y2(analytic)= = 0.99916794527147601592426506870898 y2(numeric) = = 0.99916794526454800886271077297207 absolute error = 6.92800706155429573691e-12 relative error = 6.9337763429469725032230044974910e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.54 y1(analytic)= = 0.030791459082466157622476807076397 y1(numeric) = = 0.030791459082682001034436806571471 absolute error = 2.15843411959999495074e-13 relative error = 7.0098468338874218711500443157199e-10 % glob_h = 0.01 y2(analytic)= = 0.99952583060547905600596353844003 y2(numeric) = = 0.99952583059850441101138260139486 absolute error = 6.97464499458093704517e-12 relative error = 6.9779537266745094620414388854546e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.55 y1(analytic)= = 0.020794827803092473643912774695556 y1(numeric) = = 0.02079482780338003473121531375229 absolute error = 2.87561087302539056734e-13 relative error = 1.3828490912522719377937631928953e-09 % glob_h = 0.01 y2(analytic)= = 0.99978376418935696389761134763447 y2(numeric) = = 0.9997837641823364084064430706932 absolute error = 7.02055549116827694127e-12 relative error = 7.0220739150136852437007521046027e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.56 y1(analytic)= = 0.010796117058267445823920663760906 y1(numeric) = = 0.010796117058627664167039055060642 absolute error = 3.60218343118391299736e-13 relative error = 3.3365546258369202625439653570591e-09 % glob_h = 0.01 y2(analytic)= = 0.99994172022996629574517002341348 y2(numeric) = = 0.99994172022290057147005027394332 absolute error = 7.06572427511974947016e-12 relative error = 7.0661360879059794892776298947074e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.57 y1(analytic)= = 0.00079632671073332548540853364535419 y1(numeric) = = 0.0007963267111671329541118806175618 absolute error = 4.3380746870334697220761e-13 relative error = 5.4476066525994097689425496179003e-08 % glob_h = 0.01 y2(analytic)= = 0.99999968293183462021052992382333 y2(numeric) = = 0.99999968292472448306215422898359 absolute error = 7.11013714837569483974e-12 relative error = 7.1101394027745508720188296376501e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.58 y1(analytic)= = -0.0092035432688082648053890569827275 y1(numeric) = = -0.0092035432682999442420103842651694 absolute error = 5.083205633786727175581e-13 relative error = 5.5230963611745305645365125127259e-09 % glob_h = 0.01 y2(analytic)= = 0.99995764649874005255179423225172 y2(numeric) = = 0.99995764649158627255839296487375 absolute error = 7.15377999340126737797e-12 relative error = 7.1540829938643617808290560252569e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=2.24 NO POLE NO POLE x[1] = = 1.59 y1(analytic)= = -0.019202492901692568095027346243403 y1(numeric) = = -0.019202492901108818557691991581087 absolute error = 5.83749537335354662316e-13 relative error = 3.0399674684108392137276489504309e-09 % glob_h = 0.01 y2(analytic)= = 0.99981561513429087198158434374551 y2(numeric) = = 0.99981561512709423320601854610307 absolute error = 7.19663877556579764244e-12 relative error = 7.1979659715548416551047048663845e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.6 y1(analytic)= = -0.029199522301288726205770462946499 y1(numeric) = = -0.029199522300628640093263534738551 absolute error = 6.60086112506928207948e-13 relative error = 2.2606058609314823886998760895380e-09 % glob_h = 0.01 y2(analytic)= = 0.99957360304150516434211382554623 y2(numeric) = = 0.99957360303426646479660055155947 absolute error = 7.23869954551327398676e-12 relative error = 7.2417874216439291161373495912728e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.61 y1(analytic)= = -0.039193631772987609585327609601018 y1(numeric) = = -0.03919363177225028776185680924213 absolute error = 7.37321823470800358888e-13 relative error = 1.8812286336245195373684714183110e-09 % glob_h = 0.01 y2(analytic)= = 0.9992316344213905321324131478443 y2(numeric) = = 0.99923163441411058369088953800884 absolute error = 7.27994844152360983546e-12 relative error = 7.2855464046022681855459160009810e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.62 y1(analytic)= = -0.049183821914170445143744274712327 y1(numeric) = = -0.049183821913354997125366307609217 absolute error = 8.15448018377967103110e-13 relative error = 1.6579598466361289677187950250195e-09 % glob_h = 0.01 y2(analytic)= = 0.9987897434705240139155188912468 y2(numeric) = = 0.99878974346320364222365452733767 absolute error = 7.32037169186436390913e-12 relative error = 7.3292419547962654294110398414511e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.63 y1(analytic)= = -0.059169093714148245297971697419802 y1(numeric) = = -0.059169093713253789438060672863683 absolute error = 8.94455859911024556119e-13 relative error = 1.5116943724577385712907163289242e-09 % glob_h = 0.01 y2(analytic)= = 0.9982479743776324551116699849331 y2(numeric) = = 0.99824797437027249949453740325862 absolute error = 7.35995561713258167448e-12 relative error = 7.3728730796786425655938420879439e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.64 y1(analytic)= = -0.069148448654062044364492707456605 y1(numeric) = = -0.069148448653087708038222338671816 absolute error = 9.74336326270368784789e-13 relative error = 1.4090501598160330415154112670958e-09 % glob_h = 0.01 y2(analytic)= = 0.99760638131917367213758197436794 y2(numeric) = = 0.99760638131177498550499554699778 absolute error = 7.39868663258642737016e-12 relative error = 7.4164387589450426513300535951000e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.65 y1(analytic)= = -0.079120888806733952359614597341276 y1(numeric) = = -0.079120888805678872147426121896854 absolute error = 1.055080212188475444422e-12 relative error = 1.3335039938260626829108559729873e-09 % glob_h = 0.01 y2(analytic)= = 0.99686502845391885177170304020219 y2(numeric) = = 0.99686502844648230052123676312495 absolute error = 7.43655125046627707724e-12 relative error = 7.4599379436551671382014687364238e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.66 y1(analytic)= = -0.089085416936459041185257931650621 y1(numeric) = = -0.089085416935322363055285785059341 absolute error = 1.136678129972146591280e-12 relative error = 1.2759418646296422297539146767168e-09 % glob_h = 0.01 y2(analytic)= = 0.99602398991653672750100059061296 y2(numeric) = = 0.99602398990906319141869564614784 absolute error = 7.47353608230494446512e-12 relative error = 7.5033695553168355342285531364444e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.67 y1(analytic)= = -0.099041036598728084094782342448611 y1(numeric) = = -0.0990410365975089635842097341745 absolute error = 1.219120510572608274111e-12 relative error = 1.2309246272451318428811477076674e-09 % glob_h = 0.01 y2(analytic)= = 0.99508334981018017442629724653424 y2(numeric) = = 0.9950833498026705465850705344876 absolute error = 7.50962784122671204664e-12 relative error = 7.5467324849312688133924156096679e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.68 y1(analytic)= = -0.10898675223987117624800473417282 y1(numeric) = = -0.10898675223856877864332139541051 absolute error = 1.30239760468333876231e-12 relative error = 1.1950054276476329772485775217173e-09 % glob_h = 0.01 y2(analytic)= = 0.99404320219807596406048786919357 y2(numeric) = = 0.99404320219053115071625302717101 absolute error = 7.54481334423484202256e-12 relative error = 7.5900255919978017073962749817608e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.69 y1(analytic)= = -0.11892156929661227207639046983309 y1(numeric) = = -0.11892156929522577259252496629733 absolute error = 1.38649948386550353576e-12 relative error = 1.1658940359316304898231392369930e-09 % glob_h = 0.01 y2(analytic)= = 0.99290365109411852003714929394559 y2(numeric) = = 0.99290365108653944052266205186199 absolute error = 7.57907951448724208360e-12 relative error = 7.6332477034761272185833248468529e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.7 y1(analytic)= = -0.12884449429552468408764285733487 y1(numeric) = = -0.12884449429405326804594198789217 absolute error = 1.47141604170086944270e-12 relative error = 1.1420092490145137418896577864470e-09 % glob_h = 0.01 y2(analytic)= = 0.99166481045246861534613339864788 y2(numeric) = = 0.99166481044485620196257343577954 absolute error = 7.61241338355996286834e-12 relative error = 7.6763976127040686960278705837970e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.71 y1(analytic)= = -0.13875453495237759764268978305111 y1(numeric) = = -0.13875453495082046064771771632361 absolute error = 1.55713699497206672750e-12 relative error = 1.1222242181176253878859917504550e-09 % glob_h = 0.01 y2(analytic)= = 0.99032680415615805121775222386113 y2(numeric) = = 0.99032680414851324912405401871359 absolute error = 7.64480209369820514754e-12 relative error = 7.7194740782687601769199375411477e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.72 y1(analytic)= = -0.14865070027136366713637828033119 y1(numeric) = = -0.148650700269720015251508216391 absolute error = 1.64365188487006394019e-12 relative error = 1.1057141889473493020989542856246e-09 % glob_h = 0.01 y2(analytic)= = 0.98888976600470145717817065708548 y2(numeric) = = 0.98888976599702522427811614086604 absolute error = 7.67623290005451621944e-12 relative error = 7.7624758228289939363801490172275e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=45.7MB, alloc=4.3MB, time=2.46 x[1] = = 1.73 y1(analytic)= = -0.15853200064419777090494835134257 y1(numeric) = = -0.15853200064246682082671963427702 absolute error = 1.73095007822871706555e-12 relative error = 1.0918616249053622086033786669133e-09 % glob_h = 0.01 y2(analytic)= = 0.98735383970071645108567767622206 y2(numeric) = = 0.98735383969300975791276381976654 absolute error = 7.70669317291385645552e-12 relative error = 7.8054015318863647977347606772285e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.74 y1(analytic)= = -0.16839744794907701506737731534509 y1(numeric) = = -0.16839744794725799429859106479503 absolute error = 1.81902076878625055006e-12 relative error = 1.0801949738195070947993553626219e-09 % glob_h = 0.01 y2(analytic)= = 0.98571917883555349712068269566555 y2(numeric) = = 0.98571917882781732672077747723157 absolute error = 7.73617039990521843398e-12 relative error = 7.8482498525027031821069876818210e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.75 y1(analytic)= = -0.17824605564949209038267694394263 y1(numeric) = = -0.17824605564758423740420341967995 absolute error = 1.90785297847352426268e-12 relative error = 1.0703479364643997735431076059690e-09 % glob_h = 0.01 y2(analytic)= = 0.98398594687393689873166293696799 y2(numeric) = = 0.9839859468661722465434634543327 absolute error = 7.76465218819948263529e-12 relative error = 7.8910193919611425223019054618997e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.76 y1(analytic)= = -0.1880768388928801010698001765041 y1(numeric) = = -0.18807683889088266551107123970521 absolute error = 1.99743555872893679889e-12 relative error = 1.0620316517902472993468614343479e-09 % glob_h = 0.01 y2(analytic)= = 0.98215431713761846242496809945596 y2(numeric) = = 0.98215431712982633615827490420153 absolute error = 7.79212626669319525443e-12 relative error = 7.9337087163680108932982137470287e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.77 y1(analytic)= = -0.19788881460910900038948584173039 y1(numeric) = = -0.1978888146070212431976460298019 absolute error = 2.08775719183981192849e-12 relative error = 1.0550152599396644141366042135846e-09 % glob_h = 0.01 y2(analytic)= = 0.98022447278804546701848144889842 y2(numeric) = = 0.98022447278022688653030349359456 absolute error = 7.81858048817795530386e-12 relative error = 7.9763163491925708230771365293891e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.78 y1(analytic)= = -0.20768100160878378462655329031263 y1(numeric) = = -0.20768100160660497823424317891674 absolute error = 2.17880639231011139589e-12 relative error = 1.0491120398265450458133751141895e-09 % glob_h = 0.01 y2(analytic)= = 0.9781966068080446715477686473056 y2(numeric) = = 0.9781966068002006687162735474631 absolute error = 7.84400283149509984250e-12 relative error = 8.0188407697414544970527224303897e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.79 y1(analytic)= = -0.21745242068136461493517026446461 y1(numeric) = = -0.21745242067909404342691595075698 absolute error = 2.27057150825431370763e-12 relative error = 1.0441693411090634435391086290080e-09 % glob_h = 0.01 y2(analytic)= = 0.97607092198252419340866043310862 y2(numeric) = = 0.97607092197465581200498505524142 absolute error = 7.86838140367537786720e-12 relative error = 8.0612804115644531459068038980455e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.8 y1(analytic)= = -0.22720209469308705531667430653058 y1(numeric) = = -0.22720209469072401459385701154351 absolute error = 2.36304072281729498707e-12 relative error = 1.0400611517289826461981931188857e-09 % glob_h = 0.01 y2(analytic)= = 0.97384763087819518653237317884336 y2(numeric) = = 0.97384763087030348209030987369806 absolute error = 7.89170444206330514530e-12 relative error = 8.1036336607881184359140045464881e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.81 y1(analytic)= = -0.23692904868467463478774985084198 y1(numeric) = = -0.23692904868221843273212980640291 absolute error = 2.45620205562004443907e-12 relative error = 1.0366825297513296531654816361879e-09 % glob_h = 0.01 y2(analytic)= = 0.97152695582231534740845126909038 y2(numeric) = = 0.97152695581440138709202537504199 absolute error = 7.91396031642589404839e-12 relative error = 8.1458988543734192140884208266149e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.82 y1(analytic)= = -0.24663230996883396256417104483087 y1(numeric) = = -0.24663230996628391919994000138014 absolute error = 2.55004336423104345073e-12 relative error = 1.0339453758322594690160037719952e-09 % glob_h = 0.01 y2(analytic)= = 0.96910912888045637458721531849805 y2(numeric) = = 0.96910912887252123705616986422869 absolute error = 7.93513753104545426936e-12 relative error = 8.1880742782934679730339962656544e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.83 y1(analytic)= = -0.25631090822752264682983758361853 y1(numeric) = = -0.25631090822487809448417444976198 absolute error = 2.64455234566313385655e-12 relative error = 1.0317751842678547445863454629783e-09 % glob_h = 0.01 y2(analytic)= = 0.96659439183329760489723892974281 y2(numeric) = = 0.96659439182534238017044276757604 absolute error = 7.95522472679616216677e-12 relative error = 8.2301581656270867802164756451646e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.84 y1(analytic)= = -0.2659638756089802903802829832816 y1(numeric) = = -0.26596387560624057384238728586245 absolute error = 2.73971653789569741915e-12 relative error = 1.0301085181671907788166387282427e-09 % glob_h = 0.01 y2(analytic)= = 0.96398299615244814699489367172712 y2(numeric) = = 0.96398299614447393631168957334618 absolute error = 7.97421068320409838094e-12 relative error = 8.2721486945637209567413698171458e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.85 y1(analytic)= = -0.2755902468245128601219498354748 y1(numeric) = = -0.2755902468216773368005278703548 absolute error = 2.83552332142196512000e-12 relative error = 1.0288910272022567460811236416021e-09 % glob_h = 0.01 y2(analytic)= = 0.96127520297529993001245916863613 y2(numeric) = = 0.96127520296730784569196871332858 absolute error = 7.99208432049045530755e-12 relative error = 8.3140439863149291867164409908150e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.86 y1(analytic)= = -0.28518905924502075207093548828912 y1(numeric) = = -0.28518905924208879215011421687003 absolute error = 2.93195992082127141909e-12 relative error = 1.0280758766072692060627074272112e-09 % glob_h = 0.01 y2(analytic)= = 0.9584712830789141819789777659032 y2(numeric) = = 0.95847128307090534727738014791015 absolute error = 8.00883470159761799305e-12 relative error = 8.3558421029273795663129789407415e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=49.5MB, alloc=4.3MB, time=2.67 x[1] = = 1.87 y1(analytic)= = -0.29475935299726089912514806480989 y1(numeric) = = -0.29475935299423188571879199958177 absolute error = 3.02901340635606522812e-12 relative error = 1.0276224912137776489036505092389e-09 % glob_h = 0.01 y2(analytic)= = 0.95557151685294394934425049217263 y2(numeric) = = 0.95557151684491949831005266813726 absolute error = 8.02445103419782403537e-12 relative error = 8.3975410449919608232379674912744e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.88 y1(analytic)= = -0.30430017105983329547931375952224 y1(numeric) = = -0.30430017105670662478372027357233 absolute error = 3.12667069559348594991e-12 relative error = 1.0274955432012233425625094626695e-09 % glob_h = 0.01 y2(analytic)= = 0.95257619427159536533145742581513 y2(numeric) = = 0.9525761942635564426587733156852 absolute error = 8.03892267268411012993e-12 relative error = 8.4391387492432748726097327614481e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.89 y1(analytic)= = -0.31381055935888233911038241555123 y1(numeric) = = -0.31381055935565742055533110598459 absolute error = 3.22491855505130956664e-12 relative error = 1.0276641301171782745134164453177e-09 % glob_h = 0.01 y2(analytic)= = 0.94948561486463047096820167213832 y2(numeric) = = 0.94948561485657823184805841714207 absolute error = 8.05223912014325499625e-12 relative error = 8.4806330860434092021490844056587e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.9 y1(analytic)= = -0.32328956686350342227883369508031 y1(numeric) = = -0.32328956686017967867696562866762 absolute error = 3.32374360186806641269e-12 relative error = 1.0281011027093828961705654560588e-09 % glob_h = 0.01 y2(analytic)= = 0.94630008768741448848970961163496 y2(numeric) = = 0.94630008767935009845939918108034 absolute error = 8.06439003031043055462e-12 relative error = 8.5220218567434933133093394536373e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.91 y1(analytic)= = -0.33273624568084522946633893939753 y1(numeric) = = -0.33273624567742209716084181045374 absolute error = 3.42313230549712894379e-12 relative error = 1.0287825116535507851309727369170e-09 % glob_h = 0.01 y2(analytic)= = 0.94301993129001054236188657694821 y2(numeric) = = 0.94301993128193517715238130155555 absolute error = 8.07536520950527539266e-12 relative error = 8.5633027909161204206375982798798e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.92 y1(analytic)= = -0.34214965115089823259923660315905 y1(numeric) = = -0.3421496511473751616098120386448 absolute error = 3.52307098942456451425e-12 relative error = 1.0296871493435440635855361737654e-09 % glob_h = 0.01 y2(analytic)= = 0.93964547368532491842637133968703 y2(numeric) = = 0.93964547367723976380782223291527 absolute error = 8.08515461854910677176e-12 relative error = 8.6044735434512614764572955907035e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.93 y1(analytic)= = -0.35152884194095990478728906471187 y1(numeric) = = -0.35152884193733635895437851981408 absolute error = 3.62354583291054489779e-12 relative error = 1.0307961682185747754248917434174e-09 % glob_h = 0.01 y2(analytic)= = 0.93617705231630604661512937274878 y2(numeric) = = 0.93617705230821229824046638307992 absolute error = 8.09374837466298966886e-12 relative error = 8.6455316915078107667964415258509e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.94 y1(analytic)= = -0.36087288013976720613506768584073 y1(numeric) = = -0.36087288013604266326231358480499 absolute error = 3.72454287275410103574e-12 relative error = 1.0320927611162062992391116323809e-09 % glob_h = 0.01 y2(analytic)= = 0.9326150140222004873089793388657 y2(numeric) = = 0.93261501401409935055563295523232 absolute error = 8.10113675334638363338e-12 relative error = 8.6864747313123780155524387036859e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.95 y1(analytic)= = -0.37018083135128692845582845913069 y1(numeric) = = -0.37018083134746088045074745086099 absolute error = 3.82604800508100826970e-12 relative error = 1.0335618922013388761602233908443e-09 % glob_h = 0.01 y2(analytic)= = 0.92895971500386929571329703509148 y2(numeric) = = 0.92895971499576198552306094453251 absolute error = 8.10731019023609055897e-12 relative error = 8.7273000747963780692060833667182e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.96 y1(analytic)= = -0.37945176478815451993156521544745 y1(numeric) = = -0.37945176478422647294441063133299 absolute error = 3.92804698715458411446e-12 relative error = 1.0351900693748486020477230126910e-09 % glob_h = 0.01 y2(analytic)= = 0.92521152078816823258555628949003 y2(numeric) = = 0.92521152078005597330261106066285 absolute error = 8.11225928294522882718e-12 relative error = 8.7680050460618624665678425578793e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.97 y1(analytic)= = -0.38868475336475204591463981387931 y1(numeric) = = -0.38868475336072152047543063642852 absolute error = 4.03052543920917745079e-12 relative error = 1.0369651508884439949983241903715e-09 % glob_h = 0.01 y2(analytic)= = 0.92137080619139538326395099715317 y2(numeric) = = 0.92137080618327940847106903548006 absolute error = 8.11597479288196167311e-12 relative error = 8.8085868776658838609276803182474e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.98 y1(analytic)= = -0.39787887378991597815247385990719 y1(numeric) = = -0.39787887378578250930616773503879 absolute error = 4.13346884630612486840e-12 relative error = 1.0388761803142726622927412922179e-09 % glob_h = 0.01 y2(analytic)= = 0.917437955281809840204735217402 y2(numeric) = = 0.91743795527369139255768750734901 absolute error = 8.11844764704771005299e-12 relative error = 8.8490427067124803462556531196272e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 1.99 y1(analytic)= = -0.40703320665926554173363571613029 y1(numeric) = = -0.40703320665502867917342376936399 absolute error = 4.23686256021194676630e-12 relative error = 1.0409132451344926442652247765118e-09 % glob_h = 0.01 y2(analytic)= = 0.91341336134122519712879327105761 y2(numeric) = = 0.91341336133310552818897868829944 absolute error = 8.11966893981458275817e-12 relative error = 8.8893695707406078484583713751417e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2 y1(analytic)= = -0.41614683654714238699756822950076 y1(numeric) = = -0.41614683654280169519626967677963 absolute error = 4.34069180129855272113e-12 relative error = 1.0430673550985472580768119390589e-09 % glob_h = 0.01 y2(analytic)= = 0.90929742682568169539601986591174 y2(numeric) = = 0.90929742681756206546133810689048 absolute error = 8.11962993468175902126e-12 relative error = 8.9295644033955300622575721280979e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.01 y1(analytic)= = -0.42521885209815239251738234016543 y1(numeric) = = -0.42521885209370745085691711759964 absolute error = 4.44494166046522256579e-12 relative error = 1.0453303371975628752510182006665e-09 % glob_h = 0.01 y2(analytic)= = 0.90509056332520095536009971027372 y2(numeric) = = 0.90509056331708263329408914887843 absolute error = 8.11832206601056139529e-12 relative error = 8.9696240298702916556155426548678e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=2.89 NO POLE NO POLE x[1] = = 2.02 y1(analytic)= = -0.4342483461183004450517028740902 y1(numeric) = = -0.4342483461137508479506207475113 absolute error = 4.54959710108212657890e-12 relative error = 1.0476947446663847588210191525331e-09 % glob_h = 0.01 y2(analytic)= = 0.90079319152262731719701352455371 y2(numeric) = = 0.90079319151451158025627556529566 absolute error = 8.11573694073795925805e-12 relative error = 9.0095451621029458256804309018323e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.03 y1(analytic)= = -0.4432344156657090830635167316961 y1(numeric) = = -0.44323441566105444010256158652312 absolute error = 4.65464296095514517298e-12 relative error = 1.0501537778748917968231725811808e-09 % glob_h = 0.01 y2(analytic)= = 0.89640574115155990703888883196757 y2(numeric) = = 0.89640574114344804069882058606902 absolute error = 8.11186634006824589855e-12 relative error = 9.0493243937141753922278042808799e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.04 y1(analytic)= = -0.45217616214091193201727020529136 y1(numeric) = = -0.45217616213615186806295845980695 absolute error = 4.76006395431174548441e-12 relative error = 1.0527012153348242766305790312763e-09 % glob_h = 0.01 y2(analytic)= = 0.8919286509533796351715256485842 y2(numeric) = = 0.89192865094527293295038301380192 absolute error = 8.10670222114263478228e-12 relative error = 9.0889581946688304435084376273772e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.05 y1(analytic)= = -0.4610726913767129021859299941674 y1(numeric) = = -0.4610726913718470575121223248548 absolute error = 4.86584467380766931260e-12 relative error = 1.0553313533444772906183610900652e-09 % glob_h = 0.01 y2(analytic)= = 0.88736236863337542355996660468034 y2(numeric) = = 0.88736236862527518684128008141495 absolute error = 8.10023671868652326539e-12 relative error = 9.1284429056436973824710931433163e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.06 y1(analytic)= = -0.4699231137276021631231096264879 y1(numeric) = = -0.46992311372263019353055544255863 absolute error = 4.97196959255418392927e-12 relative error = 1.0580389530352531564669806053660e-09 % glob_h = 0.01 y2(analytic)= = 0.8827073508159740500427975851999 y2(numeric) = = 0.88270735080788158789616341046486 absolute error = 8.09246214663417473504e-12 relative error = 9.1677747320825055518373268224514e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.07 y1(analytic)= = -0.47872654415871995327732713901173 y1(numeric) = = -0.47872654415364153021116149462978 absolute error = 5.07842306616564438195e-12 relative error = 1.0608191937821422856431510765843e-09 % glob_h = 0.01 y2(analytic)= = 0.87796406299907808617345112044384 y2(numeric) = = 0.87796406299099471517372054755019 absolute error = 8.08337099973057289365e-12 relative error = 9.2069497379177590642610698349484e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.08 y1(analytic)= = -0.48748210233435932844156884977235 y1(numeric) = = -0.48748210232917413910674173672331 absolute error = 5.18518933482711304904e-12 relative error = 1.0636676321032687057481288945757e-09 % glob_h = 0.01 y2(analytic)= = 0.87313297950751649487667680502462 y2(numeric) = = 0.87313297949944353892156660034643 absolute error = 8.07295595511020467819e-12 relative error = 9.2459638389374426766394839951786e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.09 y1(analytic)= = -0.49618891270599899883706631187045 y1(numeric) = = -0.49618891270070674631168453250345 absolute error = 5.29225252538177936700e-12 relative error = 1.0665801653084368153167657284352e-09 % glob_h = 0.01 y2(analytic)= = 0.86821458344561254282162205872751 y2(numeric) = = 0.86821458343755133294776952761557 absolute error = 8.06120987385253111194e-12 relative error = 9.2848127957729800910207338484227e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.1 y1(analytic)= = -0.50484610459985745162093852371917 y1(numeric) = = -0.50484610459445785496750060387421 absolute error = 5.39959665343791984496e-12 relative error = 1.0695529992684912311045017494849e-09 % glob_h = 0.01 y2(analytic)= = 0.86320936664887377068075931326902 y2(numeric) = = 0.86320936664082564487824540504458 absolute error = 8.04812580251390822444e-12 relative error = 9.3234922064830082954715042035604e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.11 y1(analytic)= = -0.51345281230395960347841015707169 y1(numeric) = = -0.51345281229845239785291502136463 absolute error = 5.50720562549513570706e-12 relative error = 1.0725826197705034341164021231596e-09 % glob_h = 0.01 y2(analytic)= = 0.85811782963480885223737550831068 y2(numeric) = = 0.85811782962677515526273978526446 absolute error = 8.03369697463572304622e-12 relative error = 9.3619974987055584873735842348440e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.12 y1(analytic)= = -0.52200817515470727670690188298389 y1(numeric) = = -0.52200817514909221346581228022411 absolute error = 5.61506324108960275978e-12 relative error = 1.0756657670017274241314743907283e-09 % glob_h = 0.01 y2(analytic)= = 0.85294048155287626061472733365415 y2(numeric) = = 0.85294048154485834380249882106748 absolute error = 8.01791681222851258667e-12 relative error = 9.4003239213490872506347209317166e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.13 y1(analytic)= = -0.53051133762294484181652620960972 y1(numeric) = = -0.53051133761722168862156814423953 absolute error = 5.72315319495806537019e-12 relative error = 1.0787994127706530190113999206900e-09 % glob_h = 0.01 y2(analytic)= = 0.8476778401335697467185299963159 y2(numeric) = = 0.84767784012556896779129815967853 absolute error = 8.00077892723183663737e-12 relative error = 9.4384665357904638073034285228537e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.14 y1(analytic)= = -0.5389614493995114201544499120086 y1(numeric) = = -0.5389614493936799610752296082466 absolute error = 5.83145907922030376200e-12 relative error = 1.0819807401285332267456607605302e-09 % glob_h = 0.01 y2(analytic)= = 0.84233043163664572130250663706891 y2(numeric) = = 0.84233043162866344417955695886147 absolute error = 7.98227712294967820744e-12 relative error = 9.4764202065454712625456713680547e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.15 y1(analytic)= = -0.54735766548027109140415388226403 y1(numeric) = = -0.54735766547433112701857408107478 absolute error = 5.93996438557980118925e-12 relative error = 1.0852071251012562481481930166467e-09 % glob_h = 0.01 y2(analytic)= = 0.83689879079849771787564813704379 y2(numeric) = = 0.83689879079053531248018698865093 absolute error = 7.96240539546114839286e-12 relative error = 9.5141795913746006272614097968259e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=3.10 NO POLE NO POLE x[1] = = 2.16 y1(analytic)= = -0.55569914625061260300969874398337 y1(numeric) = = -0.55569914624456395050215640904919 absolute error = 6.04865250754233493418e-12 relative error = 1.0884761202808248684991222525573e-09 % glob_h = 0.01 y2(analytic)= = 0.83138346077868319896103812034632 y2(numeric) = = 0.83138346077074204102603184483944 absolute error = 7.94115793500627550688e-12 relative error = 9.5517391307838824756988558885688e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.17 y1(analytic)= = -0.56398505756941013162446999441651 y1(numeric) = = -0.56398505756325262488181778192162 absolute error = 6.15750674265221249489e-12 relative error = 1.0917854400591814941636327254637e-09 % glob_h = 0.01 y2(analytic)= = 0.82578499310560805298105642394338 y2(numeric) = = 0.82578499309768952385370976258889 absolute error = 7.91852912734666135449e-12 relative error = 9.5890930368771861527534381864787e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.18 y1(analytic)= = -0.57221457085243670057822486766249 y1(numeric) = = -0.57221457084617019028347899588109 absolute error = 6.26651029474587178140e-12 relative error = 1.0951329473156471039102391622845e-09 % glob_h = 0.01 y2(analytic)= = 0.82010394762137421327400974608394 y2(numeric) = = 0.82010394761347969971890895546564 absolute error = 7.89451355510079061830e-12 relative error = 9.6262352815127912601784778339102e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.19 y1(analytic)= = -0.58038686315522191209020516379695 y1(numeric) = = -0.5803868631488462658139826021712 absolute error = 6.37564627622256162575e-12 relative error = 1.0985166413936255980262792689910e-09 % glob_h = 0.01 y2(analytic)= = 0.814340892425795914434327645905 y2(numeric) = = 0.8143408924179268084352738634672 absolute error = 7.86910599905378243780e-12 relative error = 9.6631595837130681220022256861557e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.2 y1(analytic)= = -0.58850111725534570852414261265493 y1(numeric) = = -0.58850111724886081081381079622248 absolute error = 6.48489771033181643245e-12 relative error = 1.1019346472231204957976505557945e-09 % glob_h = 0.01 y2(analytic)= = 0.80849640381959018430403691041612 y2(numeric) = = 0.80849640381174788286459553400932 absolute error = 7.84230143944137640680e-12 relative error = 9.6998593962717566431602130164528e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.21 y1(analytic)= = -0.59655652173415993337760917751863 y1(numeric) = = -0.59655652172756568584413174116702 absolute error = 6.59424753347743635161e-12 relative error = 1.1053852054635642921105120349302e-09 % glob_h = 0.01 y2(analytic)= = 0.80257106624674725251897404255597 y2(numeric) = = 0.80257106623893315746176609417081 absolute error = 7.81409505720794838516e-12 relative error = 9.7363278914985657211680159185541e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.22 y1(analytic)= = -0.60455227105792951991771443750015 y1(numeric) = = -0.60455227105122584132017675555314 absolute error = 6.70367859753768194701e-12 relative error = 1.1088666635569252228123538821587e-09 % glob_h = 0.01 y2(analytic)= = 0.79656547223608663852085674960916 y2(numeric) = = 0.79656547222830215628561839488859 absolute error = 7.78448223523835472057e-12 relative error = 9.7725579460355825783774006131667e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.23 y1(analytic)= = -0.61248756565838519341190391068563 y1(numeric) = = -0.6124875656515720197397025207284 absolute error = 6.81317367220138995723e-12 relative error = 1.1123774675944092702907543564544e-09 % glob_h = 0.01 y2(analytic)= = 0.79048022234200476337771012718854 y2(numeric) = = 0.79048022233425130481814672048506 absolute error = 7.75345855956340670348e-12 relative error = 9.8085421246742319823031412229825e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.24 y1(analytic)= = -0.62036161201267963175076226631044 y1(numeric) = = -0.62036161200575691630344255190142 absolute error = 6.92271544731971440902e-12 relative error = 1.1159161549116324673438915514852e-09 % glob_h = 0.01 y2(analytic)= = 0.7843159250844200106020886706045 y2(numeric) = = 0.78431592507669899078154989027205 absolute error = 7.72101982053878033245e-12 relative error = 9.8442726630952020129664603894434e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.25 y1(analytic)= = -0.6281736227227390889133890573964 y1(numeric) = = -0.62817362271570680237811586235763 absolute error = 7.03228653527319503877e-12 relative error = 1.1194813473371643339188231755778e-09 % glob_h = 0.01 y2(analytic)= = 0.77807319688792124141096667558776 y2(numeric) = = 0.77807319688023407939696950583868 absolute error = 7.68716201399716974908e-12 relative error = 9.8797414494467914513120198423300e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.26 y1(analytic)= = -0.63592281659400254617912656874484 y1(numeric) = = -0.63592281658686067670577271603393 absolute error = 7.14186947335385271091e-12 relative error = 1.1230717450280598125331260983941e-09 % glob_h = 0.01 y2(analytic)= = 0.77175266202012584952506163774032 y2(numeric) = = 0.77175266201247396818268814173088 absolute error = 7.65188134237349600944e-12 relative error = 9.9149400046694615986384618184909e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.27 y1(analytic)= = -0.6436084187135405172361343481243 y1(numeric) = = -0.6436084187062890705099723388328 absolute error = 7.25144672616200929150e-12 relative error = 1.1266861208335916012329492017391e-09 % glob_h = 0.01 y2(analytic)= = 0.76535495252925351965074260193472 y2(numeric) = = 0.76535495252163834543493961574165 absolute error = 7.61517421580298619307e-12 relative error = 9.9498594614659108562989010959249e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.28 y1(analytic)= = -0.6512296605275456953713983504607 y1(numeric) = = -0.65122966052018469468338082321947 absolute error = 7.36100068801752724123e-12 relative error = 1.1303233151350255220955211520540e-09 % glob_h = 0.01 y2(analytic)= = 0.75888070818092193221665357630092 y2(numeric) = = 0.75888070817334489496346163509027 absolute error = 7.57703725319194121065e-12 relative error = 9.9844905418066417490579296962487e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.29 y1(analytic)= = -0.65878577991818769374203101818895 y1(numeric) = = -0.65878577991071718005664585615414 absolute error = 7.47051368538516203481e-12 relative error = 1.1339822311150825159949294800601e-09 % glob_h = 0.01 y2(analytic)= = 0.75233057639417073474190827797365 y2(numeric) = = 0.75233057638663326745864726391711 absolute error = 7.53746728326101405654e-12 relative error = 1.0018823532850653438478269035813e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=61.0MB, alloc=4.3MB, time=3.32 x[1] = = 2.3 y1(analytic)= = -0.66627602127982419331788057116602 y1(numeric) = = -0.66627602127224422533856685277156 absolute error = 7.57996797931371839446e-12 relative error = 1.1376618304158158131903577739458e-09 % glob_h = 0.01 y2(analytic)= = 0.7457052121767201773854062116435 y2(numeric) = = 0.74570521216922371603984538798072 absolute error = 7.49646134556082366278e-12 relative error = 1.0052848261149450749502199638023e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.31 y1(analytic)= = -0.67369963559456087744416432347103 y1(numeric) = = -0.67369963558687153167627562422859 absolute error = 7.68934576788869924244e-12 relative error = 1.1413611291480976530691528469440e-09 % glob_h = 0.01 y2(analytic)= = 0.73900527805947088675876419209826 y2(numeric) = = 0.73900527805201687006730445915274 absolute error = 7.45401669145973294552e-12 relative error = 1.0086554064989880398303236726682e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.32 y1(analytic)= = -0.68105588050715259709363616600823 y1(numeric) = = -0.68105588049935396790493803177448 absolute error = 7.79862918869813423375e-12 relative error = 1.1450791942198392533495493911875e-09 % glob_h = 0.01 y2(analytic)= = 0.73223144403025132797089867772467 y2(numeric) = = 0.73223144402284119718579505463048 absolute error = 7.41013078510362309419e-12 relative error = 1.0119929764717235743067979216377e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.33 y1(analytic)= = -0.688344020399238276754180427816 y1(numeric) = = -0.68834402039133047643286915509272 absolute error = 7.90780032131127272328e-12 relative error = 1.1488151399535312234481815945851e-09 % glob_h = 0.01 y2(analytic)= = 0.72538438746681958010284419247542 y2(numeric) = = 0.72538438745945477879849669283965 absolute error = 7.36480130434749963577e-12 relative error = 1.0152963630864441829805213166557e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.34 y1(analytic)= = -0.69556332646290213752310557206135 y1(numeric) = = -0.69556332645488529633333574800696 absolute error = 8.01684118976982405439e-12 relative error = 1.1525681249667498380311293722242e-09 % glob_h = 0.01 y2(analytic)= = 0.71846479306912612487942868679401 y2(numeric) = = 0.71846479306180809873776991748127 absolute error = 7.31802614165876931274e-12 relative error = 1.0185643349895748139405049694191e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.35 y1(analytic)= = -0.70271307677355388134712911225892 y1(numeric) = = -0.7027130767654281475820376861328 absolute error = 8.12573376509142612612e-12 relative error = 1.1563373492919795446079592569932e-09 % glob_h = 0.01 y2(analytic)= = 0.71147335279084442220249118201321 y2(numeric) = = 0.7114733527835746187974991516713 absolute error = 7.26980340499203034191e-12 relative error = 1.0217955987353995575930641564948e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.36 y1(analytic)= = -0.7097925563621205484503630346451 y1(numeric) = = -0.70979255635388608848257801333893 absolute error = 8.23445996778502130617e-12 relative error = 1.1601220517144985343869756833766e-09 % glob_h = 0.01 y2(analytic)= = 0.7044107657701761194310307129327 y2(numeric) = = 0.70441076576295598801239549076027 absolute error = 7.22013141863522217243e-12 relative error = 1.0249887948178933988748254000923e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.37 y1(analytic)= = -0.71680105728654282882471660882235 y1(numeric) = = -0.71680105727819982715433879191691 absolute error = 8.34300167037781690544e-12 relative error = 1.1639215073092007582093919064624e-09 % glob_h = 0.01 y2(analytic)= = 0.69727773825993781382969642028923 y2(numeric) = = 0.69727773825276880510566943585455 absolute error = 7.16900872402698443468e-12 relative error = 1.0281424933939957960191633697839e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.38 y1(analytic)= = -0.72373787870256867821114760736753 y1(numeric) = = -0.72373787869411733751119410174932 absolute error = 8.45134069995350561821e-12 relative error = 1.1677350251591177720479864543504e-09 % glob_h = 0.01 y2(analytic)= = 0.6900749835569363594511131070202 y2(numeric) = = 0.69007498354981992537056802865385 absolute error = 7.11643408054507836635e-12 relative error = 1.0312551896699671050604385931132e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.39 y1(analytic)= = -0.73060232693383715926915829261806 y1(numeric) = = -0.73060232692527770042845687305834 absolute error = 8.55945884070141955972e-12 relative error = 1.1715619462400861233876110455664e-09 % glob_h = 0.01 y2(analytic)= = 0.68280322193063978086250031101305 y2(numeric) = = 0.68280322192357737439623458339486 absolute error = 7.06240646626572761819e-12 relative error = 1.0343252989194503115738269669195e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.4 y1(analytic)= = -0.73739371554124549960882222733478 y1(numeric) = = -0.737393715532578161772345937534 absolute error = 8.66733783647628980078e-12 relative error = 1.1754016414575056846074455666797e-09 % glob_h = 0.01 y2(analytic)= = 0.67546318055115092656577152534128 y2(numeric) = = 0.67546318054414400148707778636275 absolute error = 7.00692507869373897853e-12 relative error = 1.0373511510984756411903984020239e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.41 y1(analytic)= = -0.74411136539159243003734439556795 y1(numeric) = = -0.7441113653828174706439761139611 absolute error = 8.77495939336828160685e-12 relative error = 1.1792535098224731631985628332227e-09 % glob_h = 0.01 y2(analytic)= = 0.66805559341649106468574980065472 y2(numeric) = = 0.66805559340954107535028653344202 absolute error = 6.94998933546326721270e-12 relative error = 1.0403309850188443249721085733810e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.42 y1(analytic)= = -0.75075460472549093874353256891074 y1(numeric) = = -0.75075460471660863356124959497359 absolute error = 8.88230518228297393715e-12 relative error = 1.1831169767557719134614122626675e-09 % glob_h = 0.01 y2(analytic)= = 0.66058120127920069250633410656023 y2(numeric) = = 0.66058120127230909363132501466994 absolute error = 6.89159887500909189029e-12 relative error = 1.0432629420370523882741547679766e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.43 y1(analytic)= = -0.7573227692245436502013552441779 y1(numeric) = = -0.7573227692155542933598242940295 absolute error = 8.98935684153095014840e-12 relative error = 1.1869914925092706572962072740236e-09 % glob_h = 0.01 y2(analytic)= = 0.6530407515722648997124970471899 y2(numeric) = = 0.65304075156543314615528876942011 absolute error = 6.83175355720827776979e-12 relative error = 1.0461450592110991854240900800295e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=64.8MB, alloc=4.3MB, time=3.54 x[1] = = 2.44 y1(analytic)= = -0.7638152020777741113106750925374 y1(numeric) = = -0.7638152020686780153312484272603 absolute error = 9.09609597942666527710e-12 relative error = 1.1908765306952442193660836466784e-09 % glob_h = 0.01 y2(analytic)= = 0.64543499833437069274006107298253 y2(numeric) = = 0.64543499832760023927606897895765 absolute error = 6.77045346399209402488e-12 relative error = 1.0489752618720914441466990460598e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.45 y1(analytic)= = -0.77023125404730734170190306733649 y1(numeric) = = -0.77023125403810483752500681359131 absolute error = 9.20250417689625374518e-12 relative error = 1.1947715869149915160416062741546e-09 % glob_h = 0.01 y2(analytic)= = 0.63776470213450375443853285563378 y2(numeric) = = 0.63776470212779605553860478430268 absolute error = 6.70769889992807133110e-12 relative error = 1.0517513555514124816718356981852e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.46 y1(analytic)= = -0.7765702835332930802042763146862 y1(numeric) = = -0.77657028352398451721418237484073 absolute error = 9.30856299009393984547e-12 relative error = 1.1986761774789008681288789014649e-09 % glob_h = 0.01 y2(analytic)= = 0.63003062999589217930819371861593 y2(numeric) = = 0.63003062998924868891542163903315 absolute error = 6.64349039277207958278e-12 relative error = 1.0544710171972742597313927108340e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.47 y1(analytic)= = -0.78283165663806523520721558406155 y1(numeric) = = -0.78283165662865098125418887214439 absolute error = 9.41425395302671191716e-12 relative error = 1.2025898382108099416718173943077e-09 % glob_h = 0.01 y2(analytic)= = 0.62223355531930478987454240485577 y2(numeric) = = 0.62223355531272696118055209207546 absolute error = 6.57782869399031278031e-12 relative error = 1.0571317856065863168664845550620e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.48 y1(analytic)= = -0.78901474722953112302319203359033 y1(numeric) = = -0.78901474722001156444300511387446 absolute error = 9.51955858018691971587e-12 relative error = 1.2065121233301357914644122137698e-09 % glob_h = 0.01 y2(analytic)= = 0.6143742578057117043045348806656 y2(numeric) = = 0.61437425779920098952528380925158 absolute error = 6.51071477925107141402e-12 relative error = 1.0597310509891195363107809118193e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.49 y1(analytic)= = -0.79511893700378415538109133257157 y1(numeric) = = -0.7951189369941596970118988794512 absolute error = 9.62445836919245312037e-12 relative error = 1.2104426044058170999668135436166e-09 % glob_h = 0.01 y2(analytic)= = 0.6064535233783148891434102397918 y2(numeric) = = 0.6064535233718727392945240033174 absolute error = 6.44214984888623647440e-12 relative error = 1.0622660435707495872288351406437e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.5 y1(analytic)= = -0.80114361554693371483350279046735 y1(numeric) = = -0.80114361553720478003006863147092 absolute error = 9.72893480343415899643e-12 relative error = 1.2143808693766223918942488321649e-09 % glob_h = 0.01 y2(analytic)= = 0.59847214410395649405185470218616 y2(numeric) = = 0.59847214409758435872353236914783 absolute error = 6.37213532832233303833e-12 relative error = 1.0647338211309419084504503004530e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.51 y1(analytic)= = -0.80708818039614603514191750787841 y1(numeric) = = -0.80708818038631306578718735611874 absolute error = 9.83296935473015175967e-12 relative error = 1.2183265216328406084622706324833e-09 % glob_h = 0.01 y2(analytic)= = 0.59043091811391282764453715502405 y2(numeric) = = 0.59043091810761215477605606980807 absolute error = 6.30067286848108521598e-12 relative error = 1.0671312553563608991636381314628e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.52 y1(analytic)= = -0.81295203709988998260266426045185 y1(numeric) = = -0.8129520370899534391166775885092 absolute error = 9.93654348598667194265e-12 relative error = 1.2222791791547891137440244370078e-09 % glob_h = 0.01 y2(analytic)= = 0.58233064952408189496642758229713 y2(numeric) = = 0.58233064951785413062027821420301 absolute error = 6.22776434614936809412e-12 relative error = 1.0694550168772840901691921115281e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.53 y1(analytic)= = -0.81873459927738171378565517255499 y1(numeric) = = -0.81873459926734207513179002667728 absolute error = 1.003963865386514587771e-11 relative error = 1.2262384737039535548260020564228e-09 % glob_h = 0.01 y2(analytic)= = 0.5741721483545724777866405874022 y2(numeric) = = 0.574172148348419065922322121225 absolute error = 6.15341186431846617720e-12 relative error = 1.0717015588360631184006715690042e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.54 y1(analytic)= = -0.82443528867722226526970435580657 y1(numeric) = = -0.82443528866708002895824925735062 absolute error = 1.014223631145509845595e-11 relative error = 1.2302040500629180638219186045761e-09 % glob_h = 0.01 y2(analytic)= = 0.56595623044870279873476574798203 y2(numeric) = = 0.56595623044262518098227319627467 absolute error = 6.07761775249255170736e-12 relative error = 1.0738670988168254602086581226101e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.55 y1(analytic)= = -0.83005353523522221166431047583229 y1(numeric) = = -0.83005353522497789375335790601788 absolute error = 1.024431791095256981441e-11 relative error = 1.2341755653205566739550696309519e-09 % glob_h = 0.01 y2(analytic)= = 0.55768371739141686934577028176624 y2(numeric) = = 0.55768371738541648477880398162741 absolute error = 6.00038456696630013883e-12 relative error = 1.0759475989425130967645288238187e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.56 y1(analytic)= = -0.83558877713140760950028812338244 y1(numeric) = = -0.8355887771210617445939444376437 absolute error = 1.034586490634368573874e-11 relative error = 1.2381526881992407240306701438614e-09 % glob_h = 0.01 y2(analytic)= = 0.54935543642712668031068338313728 y2(numeric) = = 0.54935543642120496521961181918801 absolute error = 5.92171509107156394927e-12 relative error = 1.0779387439186821802173728460442e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.57 y1(analytic)= = -0.84104046084620152644236372156713 y1(numeric) = = -0.84104046083575466768627069102047 absolute error = 1.044685875609303054666e-11 relative error = 1.2421350984210752932557494219236e-09 % glob_h = 0.01 y2(analytic)= = 0.54097222037698844964557254874584 y2(numeric) = = 0.54097222037114683731017951885449 absolute error = 5.84161233539302989135e-12 relative error = 1.0798359167726160152905559137674e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.58 y1(analytic)= = -0.84640804121577553771763249456923 y1(numeric) = = -0.84640804120522825679179602433021 absolute error = 1.054728092583647023902e-11 relative error = 1.2461224861104128787447242972860e-09 % glob_h = 0.01 y2(analytic)= = 0.53253490755562120108505876447165 y2(numeric) = = 0.53253490754986112154710597575125 absolute error = 5.76007953795278872040e-12 relative error = 1.0816341720004844569906246298787e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=3.75 NO POLE NO POLE x[1] = = 2.59 y1(analytic)= = -0.85169098148656565465635974540831 y1(numeric) = = -0.85169098147591854176528167263741 absolute error = 1.064711289107807277090e-11 relative error = 1.2501145512301068643995440882295e-09 % glob_h = 0.01 y2(analytic)= = 0.52404434168727600077313024887591 y2(numeric) = = 0.52404434168159888060876649849646 absolute error = 5.67712016436375037945e-12 relative error = 1.0833282057936192104446954769480e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.6 y1(analytic)= = -0.8568887533689472337977021516452 y1(numeric) = = -0.85688875335820089765781138024185 absolute error = 1.074633613989077140335e-11 relative error = 1.2541110030491628530976292985013e-09 % glob_h = 0.01 y2(analytic)= = 0.51550137182146423525772693520937 y2(numeric) = = 0.51550137181587149734977509363047 absolute error = 5.59273790795184157890e-12 relative error = 1.0849123229663873894580437972030e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.61 y1(analytic)= = -0.86200083709006349911416744872265 y1(numeric) = = -0.86200083707921856693854703247288 absolute error = 1.084493217562041624977e-11 relative error = 1.2581115596396244515942075075629e-09 % glob_h = 0.01 y2(analytic)= = 0.5069068522480533678909866995555 y2(numeric) = = 0.50690685224254643120113977287939 absolute error = 5.50693668984692667611e-12 relative error = 1.0863804001513326368346351386538e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.62 y1(analytic)= = -0.86702672144580239454661367674835 y1(numeric) = = -0.86702672143485951202702081842112 absolute error = 1.094288251959285832723e-11 relative error = 1.2621159474006932263582485872872e-09 % glob_h = 0.01 y2(analytic)= = 0.49826164241183866398876000999763 y2(numeric) = = 0.49826164240641894332971761325939 absolute error = 5.41972065904239673824e-12 relative error = 1.0877258447606370532767879888495e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.63 y1(analytic)= = -0.87196590385191656920784839019493 y1(numeric) = = -0.87196590384087640049402468053115 absolute error = 1.104016871382370966378e-11 relative error = 1.2661239006082317381391648177312e-09 % glob_h = 0.01 y2(analytic)= = 0.48956660682659942750568705361163 y2(numeric) = = 0.48956660682126833331326367795165 absolute error = 5.33109419242337565998e-12 relative error = 1.0889415491346219494721122934753e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.64 y1(analytic)= = -0.87681789039428138329890731626599 y1(numeric) = = -0.87681789038314461097517689396787 absolute error = 1.113677232373042229812e-11 relative error = 1.2701351609879351133689763160748e-09 % glob_h = 0.01 y2(analytic)= = 0.48082261498864834353055026953286 y2(numeric) = = 0.48082261498340728163578677332723 absolute error = 5.24106189476349620563e-12 relative error = 1.0900198392056146346663560538229e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.65 y1(analytic)= = -0.88158219587828590897930236605381 y1(numeric) = = -0.88158219586705323403845603771695 absolute error = 1.123267494084632833686e-11 relative error = 1.2741494773105816886771094165707e-09 % glob_h = 0.01 y2(analytic)= = 0.47203054128988257159561077839739 y2(numeric) = = 0.47203054128473294299692057554495 absolute error = 5.14962859869020285244e-12 relative error = 1.0909524168962028945192379968843e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.66 y1(analytic)= = -0.88625834387735198713231100388259 y1(numeric) = = -0.8862583438660241289467747212737 absolute error = 1.132785818553628260889e-11 relative error = 1.2781666050078879202146702678641e-09 % glob_h = 0.01 y2(analytic)= = 0.46319126493034528461814059379635 y2(numeric) = = 0.46319126492528848525352205146903 absolute error = 5.05679936461854232732e-12 relative error = 1.0917302953411662366468466202504e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.67 y1(analytic)= = -0.89084586678057648816006285842974 y1(numeric) = = -0.89084586676915418445034930955547 absolute error = 1.142230370971354887427e-11 relative error = 1.2821863058075979258939287732437e-09 % glob_h = 0.01 y2(analytic)= = 0.4543056698303063972473913211913 y2(numeric) = = 0.45430566982534381776673791443783 absolute error = 4.96257948065340675347e-12 relative error = 1.0923437258678818990608874062537e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.68 y1(analytic)= = -0.89534430583949201262204581862066 y1(numeric) = = -0.89534430582797601942248824861237 absolute error = 1.151599319955757000829e-11 relative error = 1.2862083473865345763607695281164e-09 % glob_h = 0.01 y2(analytic)= = 0.44537464454187127547089883192945 y2(numeric) = = 0.44537464453700430100843863357474 absolute error = 4.86697446246019835471e-12 relative error = 1.0927821154853903105025989913333e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.69 y1(analytic)= = -0.89975321121394135568593488432887 y1(numeric) = = -0.89975321120233244730770262223987 absolute error = 1.160890837823226208900e-11 relative error = 1.2902325030404277357443893442297e-09 % glob_h = 0.01 y2(analytic)= = 0.43639908216012626653550411876099 y2(numeric) = = 0.43639908215535627648240023005672 absolute error = 4.76999005310388870427e-12 relative error = 1.0930339334108989428930465423943e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.7 y1(analytic)= = -0.90407214201706114798252728194333 y1(numeric) = = -0.90407214200536011697392281007427 absolute error = 1.170103100860447186906e-11 relative error = 1.2942585513694167674435819443903e-09 % glob_h = 0.01 y2(analytic)= = 0.42737988023382993455605308585788 y2(numeric) = = 0.42737988022915830233319663630784 absolute error = 4.67163222285644955004e-12 relative error = 1.0930866048959735439980849112009e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.71 y1(analytic)= = -0.90830066635937017453818459371608 y1(numeric) = = -0.9083006663475778316422223570058 absolute error = 1.179234289596223671028e-11 relative error = 1.2982862759781993878106270086466e-09 % glob_h = 0.01 y2(analytic)= = 0.41831794067565893261379068110859 y2(numeric) = = 0.41831794067108702544481804480833 absolute error = 4.57190716897263630026e-12 relative error = 1.0929263902925563071368352131177e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.72 y1(analytic)= = -0.91243836139195796298962879998706 y1(numeric) = = -0.91243836138007513709889631428542 absolute error = 1.188282589073248570164e-11 relative error = 1.3023154651898679359210857748744e-09 % glob_h = 0.01 y2(analytic)= = 0.40921416967201748668244467400742 y2(numeric) = = 0.40921416966754666536701056469664 absolute error = 4.47082131543410931078e-12 relative error = 1.0925382469080784059712970710368e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=3.97 NO POLE NO POLE x[1] = = 2.73 y1(analytic)= = -0.91648481334876932225826112489279 y1(numeric) = = -0.91648481333679686036706330452348 absolute error = 1.197246189119782036931e-11 relative error = 1.3063459117725376412181113403561e-09 % glob_h = 0.01 y2(analytic)= = 0.40006947759241951035844795789445 y2(numeric) = = 0.40006947758805112904578607571672 absolute error = 4.36838131266188217773e-12 relative error = 1.0919056707225930034295236901939e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.74 y1(analytic)= = -0.92043961758798060326537325177928 y1(numeric) = = -0.92043961757591937041916123865978 absolute error = 1.206123284621201311950e-11 relative error = 1.3103774126779299747789015187264e-09 % glob_h = 0.01 y2(analytic)= = 0.39088477889845241210831170164027 y2(numeric) = = 0.39088477889418781807111461133367 absolute error = 4.26459403719709030660e-12 relative error = 1.0910105144577617763101889187006e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.75 y1(analytic)= = -0.92430237863246354409665948952671 y1(numeric) = = -0.92430237862031442333874562819322 absolute error = 1.214912075791386133349e-11 relative error = 1.3144097687911280831780921367217e-09 % glob_h = 0.01 y2(analytic)= = 0.38166099205233169857656137237778 y2(numeric) = = 0.38166099204817223198521129527718 absolute error = 4.15946659135007710060e-12 relative error = 1.0898327777704222642560800835545e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.76 y1(analytic)= = -0.9280727102093326532652331971401 y1(numeric) = = -0.92807271019709654558079416228338 absolute error = 1.223610768443903485672e-11 relative error = 1.3184427846907710058345302769471e-09 % glob_h = 0.01 y2(analytic)= = 0.37239903942505551841770059244975 y2(numeric) = = 0.3723990394210025121148827932638 absolute error = 4.05300630281779918595e-12 relative error = 1.0883503644572256541471380346578e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.77 y1(analytic)= = -0.93175023528857217636777720782907 y1(numeric) = = -0.93175023527625000062514765333646 absolute error = 1.232217574262955449261e-11 relative error = 1.3224762684189992120459113039218e-09 % glob_h = 0.01 y2(analytic)= = 0.36309984720416833112128200917246 y2(numeric) = = 0.36309984720022311039701245300172 absolute error = 3.94522072426955617074e-12 relative error = 1.0865388004559495269806300339559e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.78 y1(analytic)= = -0.93533458612073878346935166911759 y1(numeric) = = -0.93533458610833147635861113009181 absolute error = 1.240730711074053902578e-11 relative error = 1.3265100312605062752845908545126e-09 % glob_h = 0.01 y2(analytic)= = 0.35376434530114292438633931722734 y2(numeric) = = 0.35376434529730680675343826271256 absolute error = 3.83611763290105451478e-12 relative error = 1.0843709050541959676872408742657e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.79 y1(analytic)= = -0.93882540427373620697953961962409 y1(numeric) = = -0.938825404261244722948395761366 absolute error = 1.249148403114385825809e-11 relative error = 1.3305438875300905138445762151737e-09 % glob_h = 0.01 y2(analytic)= = 0.34439346725839004176626159556229 y2(numeric) = = 0.34439346725466433673630477639065 absolute error = 3.72570502995681917164e-12 relative error = 1.0818164059893486040981875050055e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.8 y1(analytic)= = -0.94222234066865815258678811736615 y1(numeric) = = -0.94222234065608346377375978782005 absolute error = 1.257468881302832954610e-11 relative error = 1.3345776543681364270736701697218e-09 % glob_h = 0.01 y2(analytic)= = 0.33498815015590491954385375271242 y2(numeric) = = 0.33498815015229092840363278196349 absolute error = 3.61399114022097074893e-12 relative error = 1.0788414869418526585813823930750e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.81 y1(analytic)= = -0.94552505561469589898972047835884 y1(numeric) = = -0.94552505560203899515462438298046 absolute error = 1.265690383509609537838e-11 relative error = 1.3386111515434889799322240976315e-09 % glob_h = 0.01 y2(analytic)= = 0.32554933451756006810510128120633 y2(numeric) = = 0.32554933451405908369362489118668 absolute error = 3.50098441147639001965e-12 relative error = 1.0754082531498916634980861955054e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.82 y1(analytic)= = -0.94873321884310709569453606376004 y1(numeric) = = -0.9487332188303689841462812441333 absolute error = 1.273811154825481962674e-11 relative error = 1.3426442012632144493920957204593e-09 % glob_h = 0.01 y2(analytic)= = 0.31607796421705366845541285602457 y2(numeric) = = 0.3160779642136669749414805603205 absolute error = 3.38669351393229570407e-12 relative error = 1.0714740973232230353396049456302e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.83 y1(analytic)= = -0.95184650954024236202702511272453 y1(numeric) = = -0.95184650952742406754871977247765 absolute error = 1.281829447830534024688e-11 relative error = 1.3466766279887698388320270501934e-09 % glob_h = 0.01 y2(analytic)= = 0.3065749863835229889603130778681 y2(numeric) = = 0.30657498638025186162069281233865 absolute error = 3.27112733962026552945e-12 relative error = 1.0669909434581560973025488896945e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.84 y1(analytic)= = -0.95486461637962638472681949358624 y1(numeric) = = -0.95486461636672894949819507719615 absolute error = 1.289743522862441639009e-11 relative error = 1.3507082582581289682073707388733e-09 % glob_h = 0.01 y2(analytic)= = 0.29704135130683226089025606809731 y2(numeric) = = 0.29704135130367796588849733343576 absolute error = 3.15429500175873466155e-12 relative error = 1.0619043402143931017801023179351e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.85 y1(analytic)= = -0.95778723755309030604085410717493 y1(numeric) = = -0.95778723754011478955801189905455 absolute error = 1.297551648284220812038e-11 relative error = 1.3547389205134374200120674307972e-09 % glob_h = 0.01 y2(analytic)= = 0.28747801234254448390307892669172 y2(numeric) = = 0.2874780123395082780689929170032 absolute error = 3.03620583408600968852e-12 relative error = 1.0561523677394214105031624733061e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.86 y1(analytic)= = -0.96061408080095228910317316639277 y1(numeric) = = -0.96061408078789976809565903918398 absolute error = 1.305252100751412720879e-11 relative error = 1.3587684449337907107796311229331e-09 % glob_h = 0.01 y2(analytic)= = 0.27788592581658666420435690975324 y2(numeric) = = 0.27788592581366979481419506933081 absolute error = 2.91686939016184042243e-12 relative error = 1.0496643115661297474021087580734e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=76.2MB, alloc=4.4MB, time=4.19 x[1] = = 2.87 y1(analytic)= = -0.96334486344124324256969375873794 y1(numeric) = = -0.96334486342811481091490706093793 absolute error = 1.312843165478669780001e-11 relative error = 1.3627966632727504992522833289426e-09 % glob_h = 0.01 y2(analytic)= = 0.26826605092961801878239892098714 y2(numeric) = = 0.26826605092682172333976132511997 absolute error = 2.79629544263759586717e-12 relative error = 1.0423590435493564608444899037357e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.88 y1(analytic)= = -0.96597931239797478195981790476552 y1(numeric) = = -0.9659793123847715505947608386504 absolute error = 1.320323136505706611512e-11 relative error = 1.3668234087002324574182494632833e-09 % glob_h = 0.01 y2(analytic)= = 0.25861934966111070881776692011768 y2(numeric) = = 0.25861934965843621483527182533531 absolute error = 2.67449398249509478237e-12 relative error = 1.0341430314474515427607123238943e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.89 y1(analytic)= = -0.96851716422844660093231550720928 y1(numeric) = = -0.9685171642151696977626897084405 absolute error = 1.327690316962579876878e-11 relative error = 1.3708485156484167306765552306928e-09 % glob_h = 0.01 y2(analytic)= = 0.24894678667315269411404584058049 y2(numeric) = = 0.24894678667060121889579169522957 absolute error = 2.55147521825414535092e-12 relative error = 1.0249078738276823489747606342793e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.9 y1(analytic)= = -0.97095816514959052178110666934553 y1(numeric) = = -0.97095816513624109158776405960692 absolute error = 1.334943019334260973861e-11 relative error = 1.3748718196613477996507907127547e-09 % glob_h = 0.01 y2(analytic)= = 0.23924932921398232818425691873958 y2(numeric) = = 0.23924932921155507860910806620678 absolute error = 2.42724957514885253280e-12 relative error = 1.0145272227609648014824756486960e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.91 y1(analytic)= = -0.97330207106334859076784710660275 y1(numeric) = = -0.97330207104992779511060245007264 absolute error = 1.342079565724465653011e-11 relative error = 1.3788931572479051209990878659332e-09 % glob_h = 0.01 y2(analytic)= = 0.22952794702126434045301822382699 y2(numeric) = = 0.22952794701896251275874546806813 absolute error = 2.30182769427275575886e-12 relative error = 1.0028529092622893986811413659110e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.92 y1(analytic)= = -0.97554864758108268050293173515827 y1(numeric) = = -0.97554864756759169762174468852735 absolute error = 1.349098288118704663092e-11 relative error = 1.3829123657378392517092032567139e-09 % glob_h = 0.01 y2(analytic)= = 0.21978361222511687789562909306458 y2(numeric) = = 0.21978361222294165746393622937959 absolute error = 2.17522043169286368499e-12 relative error = 9.8971001962824206774010228494086e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.93 y1(analytic)= = -0.97769767004701315843501960467633 y1(numeric) = = -0.97769767003345318314855440873209 absolute error = 1.355997528646519594424e-11 relative error = 1.3869292831405803271450403808392e-09 % glob_h = 0.01 y2(analytic)= = 0.21001729925089930332910403425911 y2(numeric) = = 0.21001729924885186447157137747017 absolute error = 2.04743885753265678894e-12 relative error = 9.7489057560285218530086495638581e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.94 y1(analytic)= = -0.97974892356068427760176338132832 y1(numeric) = = -0.97974892354705652120333469979531 absolute error = 1.362775639842868153301e-11 relative error = 1.3909437480065368367496186463022e-09 % glob_h = 0.01 y2(analytic)= = 0.20022998472177047149431709442312 y2(numeric) = = 0.20022998471985197723929296177392 absolute error = 1.91849425502413264920e-12 relative error = 9.5814533357227984270056101120045e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.95 y1(analytic)= = -0.98170220299845404312138940470197 y1(numeric) = = -0.98170220298475973327230317300929 absolute error = 1.369430984908623169268e-11 relative error = 1.3949555992906126853950634232525e-09 % glob_h = 0.01 y2(analytic)= = 0.19042264736102722702044731405738 y2(numeric) = = 0.19042264735923882890091834126178 absolute error = 1.78839811952897279560e-12 relative error = 9.3917301555959491551489686415815e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.96 y1(analytic)= = -0.98355731303400640545638732297616 y1(numeric) = = -0.98355731302024678607668582587342 absolute error = 1.375961937970149710274e-11 relative error = 1.3989646762176795998011942755508e-09 % glob_h = 0.01 y2(analytic)= = 0.18059626789423289034054450880135 y2(numeric) = = 0.18059626789257572818301559473503 absolute error = 1.65716215752891406632e-12 relative error = 9.1760598203471147675121212446437e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.97 y1(analytic)= = -0.98531406815788372924707637480614 y1(numeric) = = -0.98531406814406006040369712722173 absolute error = 1.382366884337924758441e-11 relative error = 1.4029708181497500892747789649746e-09 % glob_h = 0.01 y2(analytic)= = 0.17075182895114551862806449866797 y2(numeric) = = 0.17075182894962072034247908722427 absolute error = 1.52479828558541144370e-12 relative error = 8.9299089500334284217388279944853e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.98 y1(analytic)= = -0.9869722926960375844844419643954 y1(numeric) = = -0.98697229268215114227680032458142 absolute error = 1.388644220764163981398e-11 relative error = 1.4069738644546034442781268658120e-09 % glob_h = 0.01 y2(analytic)= = 0.16089031496745574884655395454133 y2(numeric) = = 0.16089031496606443021728527116971 absolute error = 1.39131862926868337162e-12 relative error = 8.6476220122392932990800846749995e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 2.99 y1(analytic)= = -0.98853182082739600495858418721084 y1(numeric) = = -0.98853182081344808140158998500208 absolute error = 1.394792355699420220876e-11 relative error = 1.4109736543756236963052891964709e-09 % glob_h = 0.01 y2(analytic)= = 0.15101271208634404904629503561052 y2(numeric) = = 0.15101271208508731352423880103056 absolute error = 1.25673552205623457996e-12 relative error = 8.3220512014755087826912223167179e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3 y1(analytic)= = -0.98999249660044545727157279473126 y1(numeric) = = -0.98999249658643736017609161061602 absolute error = 1.400809709548118411524e-11 relative error = 1.4149700269026141049607412525128e-09 % glob_h = 0.01 y2(analytic)= = 0.14112000805986722210074480280811 y2(numeric) = = 0.14112000805874616059654384735204 absolute error = 1.12106150420095545607e-12 relative error = 7.9440294796848968350032980985878e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.01 memory used=80.1MB, alloc=4.4MB, time=4.41 y1(analytic)= = -0.99135417394882586223162557418242 y1(numeric) = = -0.99135417393475891508239565679643 absolute error = 1.406694714922991738599e-11 relative error = 1.4189628206433576154699322961870e-09 % glob_h = 0.01 y2(analytic)= = 0.13121319215018402315021812468485 y2(numeric) = = 0.13121319214919971382864922367598 absolute error = 9.8430932156890100887e-13 relative error = 7.5016033482538862247332917126274e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.02 y1(analytic)= = -0.99261671670593710913946653326304 y1(numeric) = = -0.99261671669181265097048269382883 absolute error = 1.412445816898383943421e-11 relative error = 1.4229518736956968708349582543580e-09 % glob_h = 0.01 y2(analytic)= = 0.12129325503062976810875799633911 y2(numeric) = = 0.12129325502978327618431113987189 absolute error = 8.4649192444685646722e-13 relative error = 6.9788870307181943118921416092751e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.03 y1(analytic)= = -0.99377999861855560232760730870843 y1(numeric) = = -0.9937799986043749875949834808067 absolute error = 1.418061473262382790173e-11 relative error = 1.4269370235199107922738433128808e-09 % glob_h = 0.01 y2(analytic)= = 0.11136118868664982569090503291726 y2(numeric) = = 0.1113611886859422032245852323762 absolute error = 7.0762246631980054106e-13 relative error = 6.3543005841193176978935827209822e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.04 y1(analytic)= = -0.99484390335945947830924495484319 y1(numeric) = = -0.99484390334522407676156745667564 absolute error = 1.423540154767749816755e-11 relative error = 1.4309181068111674807916124781829e-09 % glob_h = 0.01 y2(analytic)= = 0.10141798631660189952660831260879 y2(numeric) = = 0.10141798631603418522398993125888 absolute error = 5.6771430261838134991e-13 relative error = 5.5977674497117063853255366834677e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.05 y1(analytic)= = -0.99580832453906123102558220156492 y1(numeric) = = -0.99580832452477242757176608550454 absolute error = 1.428880345381611606038e-11 relative error = 1.4348949593718352597809934816915e-09 % glob_h = 0.01 y2(analytic)= = 0.091464642232437020053401588696418 y2(numeric) = = 0.091464642232010239063965064707671 absolute error = 4.26780989436523988747e-13 relative error = 4.6660761909717543482584082441645e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.06 y1(analytic)= = -0.99667316571604658193873927179315 y1(numeric) = = -0.99667316570170577651340049247428 absolute error = 1.434080542533877931887e-11 relative error = 1.4388674159834350880802887898136e-09 % glob_h = 0.01 y2(analytic)= = 0.081502151760269178003890088835723 y2(numeric) = = 0.081502151759984341721670796180176 absolute error = 2.84836282219292655547e-13 relative error = 3.4948314377896606811825289403657e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.07 y1(analytic)= = -0.99743834040701853109211366272677 y1(numeric) = = -0.99743834039262713851847014015858 absolute error = 1.439139257364352256819e-11 relative error = 1.4428353102780183366741315857927e-09 % glob_h = 0.01 y2(analytic)= = 0.071531511140843542442340790318903 y2(numeric) = = 0.071531511140701648307919656111702 absolute error = 1.41894134421134207201e-13 relative error = 1.9836591197094750281880971776739e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.08 y1(analytic)= = -0.99810377209514562474111853735979 y1(numeric) = = -0.99810377208070507459143353550929 absolute error = 1.444055014968500185050e-11 relative error = 1.4467984746087540487812651717038e-09 % glob_h = 0.01 y2(analytic)= = 0.061553717429913216445629637135705 y2(numeric) = = 0.061553717429915247749495003194979 absolute error = 2.031303865366059274e-15 relative error = 3.3000506714788731408528552174901e-12 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.09 y1(analytic)= = -0.99866939423781357473474351808576 y1(numeric) = = -0.99866939422332531118832510202551 absolute error = 1.448826354641841606025e-11 relative error = 1.4507567399195092982234908767898e-09 % glob_h = 0.01 y2(analytic)= = 0.051569768398534492669958510574615 y2(numeric) = = 0.051569768398681418357268592260546 absolute error = 1.46925687310081685931e-13 relative error = 2.8490662625170333986315250315855e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.1 y1(analytic)= = -0.99913515027327946449237605454147 y1(numeric) = = -0.99913515025874494619114673054972 absolute error = 1.453451830122932399175e-11 relative error = 1.4547099356132051274333451814336e-09 % glob_h = 0.01 y2(analytic)= = 0.041580662433290579194698271596673 y2(numeric) = = 0.041580662433583353671473428371591 absolute error = 2.92774476775156774918e-13 relative error = 7.0411210317985164562807898133732e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.11 y1(analytic)= = -0.99950099362632787616083083671683 y1(numeric) = = -0.99950099361174857606248181960876 absolute error = 1.457930009834901710807e-11 relative error = 1.4586578894187287844766829130702e-09 % glob_h = 0.01 y2(analytic)= = 0.031587398436453773187626872703365 y2(numeric) = = 0.031587398436893336128400762345649 absolute error = 4.39562940773889642284e-13 relative error = 1.3915769025998904502335735677828e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.12 y1(analytic)= = -0.99976688771292837334358497397559 y1(numeric) = = -0.99976688769830577857232986439146 absolute error = 1.462259477125510958413e-11 relative error = 1.4626004272561805849823257765276e-09 % glob_h = 0.01 y2(analytic)= = 0.021590975726096066090998104201892 y2(numeric) = = 0.021590975726683342247956646221125 absolute error = 5.87276156958542019233e-13 relative error = 2.7200074902067861014198552974936e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.13 y1(analytic)= = -0.99993280594389387365782723913921 y1(numeric) = = -0.99993280592922948535277023047376 absolute error = 1.466438830505700866545e-11 relative error = 1.4665373731002306945869717728201e-09 % glob_h = 0.01 y2(analytic)= = 0.011592393936158169184681483118307 y2(numeric) = = 0.011592393936894068198318406672165 absolute error = 7.35899013636923553858e-13 relative error = 6.3481194452990403024616797256853e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.14 y1(analytic)= = -0.99999873172753954528511430634505 y1(numeric) = = -0.99999873171283487844624837642976 absolute error = 1.470466683886592991529e-11 relative error = 1.4704685488413574518315032761847e-09 % glob_h = 0.01 y2(analytic)= = 0.0015926529164869525405414363244433 y2(numeric) = = 0.0015926529173723687518590338444379 absolute error = 8.854162113175975199946e-13 relative error = 5.5593795870517347460763112081562e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.15 y1(analytic)= = -0.99996465847134196162819465679473 y1(numeric) = = -0.99996465845659854496004553329707 absolute error = 1.474341666814912349766e-11 relative error = 1.4743937741447345192556029744609e-09 % glob_h = 0.01 y2(analytic)= = -0.008407247367148706459141516571067 y2(numeric) = = -0.0084072473661128941948579667620562 absolute error = 1.0358122642835498090108e-12 relative error = 1.2320468508289444227345965059510e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=4.63 NO POLE NO POLE x[1] = = 3.16 y1(analytic)= = -0.99983058958259834815991709427395 y1(numeric) = = -0.99983058956781772391284911501254 absolute error = 1.478062424706797926141e-11 relative error = 1.4783128663065291475766838725920e-09 % glob_h = 0.01 y2(analytic)= = -0.01840630693305366670737927118737 y2(numeric) = = -0.018406306931866595205185111721634 absolute error = 1.187071502194159465736e-12 relative error = 6.4492649531038783399902128017033e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.17 y1(analytic)= = -0.99959653846808585554008835013528 y1(numeric) = = -0.99959653845326957934928867008388 absolute error = 1.481627619079968005140e-11 relative error = 1.4822256401073681472543150089410e-09 % glob_h = 0.01 y2(analytic)= = -0.028403525883603859571285274896733 y2(numeric) = = -0.028403525882264681499569969665057 absolute error = 1.339178071715305231676e-12 relative error = 4.7148303953642440013957813772041e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.18 y1(analytic)= = -0.99926252853272089307268415386031 y1(numeric) = = -0.99926252851787053379484207948439 absolute error = 1.485035927784207437592e-11 relative error = 1.4861319076627217632622996538814e-09 % glob_h = 0.01 y2(analytic)= = -0.03839790450523521805369524672612 y2(numeric) = = -0.038397904503743102115517807948404 absolute error = 1.492115938177438777716e-12 relative error = 3.8859306449236099200123877588687e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.19 y1(analytic)= = -0.99882859317721865656895082969948 y1(numeric) = = -0.99882859316233579611664938839355 absolute error = 1.488286045230144130593e-11 relative error = 1.4900314782699485193537625052459e-09 % glob_h = 0.01 y2(analytic)= = -0.048388443368414200108007148451169 y2(numeric) = = -0.048388443366768331220745696906041 absolute error = 1.645868887261451545128e-12 relative error = 3.4013677082569693553087296802812e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.2 y1(analytic)= = -0.99829477579475308466166072228358 y1(numeric) = = -0.99829477577983931783549790001409 absolute error = 1.491376682616282226949e-11 relative error = 1.4939241582517362108079326174177e-09 % glob_h = 0.01 y2(analytic)= = -0.058374143427579909137217414619095 y2(numeric) = = -0.058374143425779488610505256250744 absolute error = 1.800420526712158368351e-12 relative error = 3.0842774231810268542595216027790e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.21 y1(analytic)= = -0.99766112976661757757210666520424 y1(numeric) = = -0.99766112975167451189056406896846 absolute error = 1.494306568154259623578e-11 relative error = 1.4978097507956655498393644566277e-09 % glob_h = 0.01 y2(analytic)= = -0.068354006121047817548388360676863 y2(numeric) = = -0.068354006119092063260309143350706 absolute error = 1.955754288079217326157e-12 relative error = 2.8612138469481662991836350638616e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.22 y1(analytic)= = -0.99692771845688691225434273747586 y1(numeric) = = -0.99692771844191616778141976082057 absolute error = 1.497074447292297665529e-11 relative error = 1.5016880557896134718064447760178e-09 % glob_h = 0.01 y2(analytic)= = -0.078327033470865103073444147916042 y2(numeric) = = -0.078327033468753249644958846356085 absolute error = 2.111853428485301559957e-12 relative error = 2.6961999387744419467294081198143e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.23 y1(analytic)= = -0.99609461520608088772070849458495 y1(numeric) = = -0.99609461519108409689134038414762 absolute error = 1.499679082936811043733e-11 relative error = 1.5055588696527027559115803147455e-09 % glob_h = 0.01 y2(analytic)= = -0.088292228182607612405875728529723 y2(numeric) = = -0.088292228180338911373454393420146 absolute error = 2.268701032421335109577e-12 relative error = 2.5695365029515008406400502154682e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.24 y1(analytic)= = -0.99516190332383033417882384374247 y1(numeric) = = -0.99516190330880914162210238254073 absolute error = 1.502119255672146120174e-11 relative error = 1.5094219851614933598420617194061e-09 % glob_h = 0.01 y2(analytic)= = -0.098248593745108472540154959437637 y2(numeric) = = -0.098248593742682192526586358289329 absolute error = 2.426280013568601148308e-12 relative error = 2.4695315434877651486866590411593e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.25 y1(analytic)= = -0.9941296760805462193730292251716 y1(numeric) = = -0.99412967606550228173324506413232 absolute error = 1.504393763978416103928e-11 relative error = 1.5132771912710986683267229819228e-09 % glob_h = 0.01 y2(analytic)= = -0.10819513453010837703583084256083 y2(numeric) = = -0.10819513452752380391918331520994 absolute error = 2.58457311664752735089e-12 relative error = 2.3888071565069280315465427383090e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.26 y1(analytic)= = -0.99299803669809268521269456717166 y1(numeric) = = -0.99299803668302767096822055011838 absolute error = 1.506501424447401705328e-11 relative error = 1.5171242729308966607425530095087e-09 % glob_h = 0.01 y2(analytic)= = -0.11813085589181758226072311033608 y2(numeric) = = -0.11813085588907401934143016083533 absolute error = 2.74356291929294950075e-12 relative error = 2.3224778137605827144217923202466e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.27 y1(analytic)= = -0.99176709833946494737596174049474 y1(numeric) = = -0.99176709832438053665599687945973 absolute error = 1.508441071996486103501e-11 relative error = 1.5209630108944917580305905973543e-09 % glob_h = 0.01 y2(analytic)= = -0.12805476426637965749655689075362 y2(numeric) = = -0.1280547642634764256626012399167 absolute error = 2.90323183395565083692e-12 relative error = 2.2671798668234981658664967246925e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.28 y1(analytic)= = -0.99043698409747309009035841613171 y1(numeric) = = -0.99043698408237097448955248338647 absolute error = 1.510211560080593274524e-11 relative error = 1.5247931815235677541825205573751e-09 % glob_h = 0.01 y2(analytic)= = -0.13796586727122704261491407058525 y2(numeric) = = -0.13796586726816348050508409952872 absolute error = 3.06356210982997105653e-12 relative error = 2.2205217641312075725631528369306e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.29 y1(analytic)= = -0.98900782698243288770137512553948 y1(numeric) = = -0.98900782696731477009235413610449 absolute error = 1.511811760902098943499e-11 relative error = 1.5286145565852557070570543165310e-09 % glob_h = 0.01 y2(analytic)= = -0.14786317380431847785052978374264 y2(numeric) = = -0.14786317380109394201572250841568 absolute error = 3.22453583480727532696e-12 relative error = 2.1807565412295376002222826678261e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=4.85 NO POLE NO POLE x[1] = = 3.3 y1(analytic)= = -0.98747976990886488393659105110285 y1(numeric) = = -0.98747976989373247828040421466288 absolute error = 1.513240565618683643997e-11 relative error = 1.5324269030426228860004694261671e-09 % glob_h = 0.01 y2(analytic)= = -0.15774569414324838201165427760248 y2(numeric) = = -0.1577456941398622470741992074803 absolute error = 3.38613493745507012218e-12 relative error = 2.1465783619932797341601956062396e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.31 y1(analytic)= = -0.98585296568120305894633807058553 y1(numeric) = = -0.98585296566605809010084709466188 absolute error = 1.514496884549097592365e-11 relative error = 1.5362299828378697717978285690008e-09 % glob_h = 0.01 y2(analytic)= = -0.16761244004421826827224999431698 y2(numeric) = = -0.16761244004066992708322844513549 absolute error = 3.54834118902154918149e-12 relative error = 2.1169915479337047891694772685463e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.32 y1(analytic)= = -0.98412757697851451324228958473119 y1(numeric) = = -0.98412757696335871676852151160599 absolute error = 1.515579647376807312520e-11 relative error = 1.5400235526678015935401495200703e-09 % glob_h = 0.01 y2(analytic)= = -0.17746242484086030048692055230841 y2(numeric) = = -0.17746242483714916428145520291229 absolute error = 3.71113620546534939612e-12 relative error = 2.0912236541303413584309270427739e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.33 y1(analytic)= = -0.98230377633823169655284671485927 y1(numeric) = = -0.98230377632306681851933177307053 absolute error = 1.516487803351494178874e-11 relative error = 1.5438073637511188749433060426360e-09 % glob_h = 0.01 y2(analytic)= = -0.18729466354290310775529282413595 y2(numeric) = = -0.18729466353902860630578253117554 absolute error = 3.87450144951029296041e-12 relative error = 2.0686662269065508425353144858121e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.34 y1(analytic)= = -0.98038174613889880835887990106991 y1(numeric) = = -0.98038174612372660514399614826001 absolute error = 1.517220321488375280990e-11 relative error = 1.5475811615870478496311251099929e-09 % glob_h = 0.01 y2(analytic)= = -0.19710817293466999073661691059272 y2(numeric) = = -0.19710817293063157250389202191281 absolute error = 4.03841823272488867991e-12 relative error = 2.0488334768662239998226750167408e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.35 y1(analytic)= = -0.97836167858193409545539437527153 y1(numeric) = = -0.97836167856675633354774120273675 absolute error = 1.517776190765317253478e-11 relative error = 1.5513446857048062823479074115515e-09 % glob_h = 0.01 y2(analytic)= = -0.20690197167339966997603411602551 y2(numeric) = = -0.20690197166919680225840775411633 absolute error = 4.20286771762636190918e-12 relative error = 2.0313328498680049800270321749856e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.36 y1(analytic)= = -0.97624377567240987029416530777832 y1(numeric) = = -0.9762437756572283260909881681948 absolute error = 1.518154420317713958352e-11 relative error = 1.5550976694033730828897927090262e-09 % glob_h = 0.01 y2(analytic)= = -0.21667508038737974424961398190553 y2(numeric) = = -0.21667508038301191332980500270736 absolute error = 4.36783091980897919817e-12 relative error = 2.0158436826237743149558421256372e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.37 y1(analytic)= = -0.97402824919885217208949176597085 y1(numeric) = = -0.97402824918366863169318077442392 absolute error = 1.518354039631099154693e-11 relative error = 1.5588398394810009937120091365701e-09 % glob_h = 0.01 y2(analytic)= = -0.22642652177388304566410348430857 y2(numeric) = = -0.22642652176934975695400705395118 absolute error = 4.53328871009643035739e-12 relative error = 2.0021014652265520437904521374695e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.38 y1(analytic)= = -0.97171532071206209070412534999057 y1(numeric) = = -0.97171532069687834971681069457161 absolute error = 1.518374098731465541896e-11 relative error = 1.5625709159538804313679234401172e-09 % glob_h = 0.01 y2(analytic)= = -0.23615532069689709795749177758963 y2(numeric) = = -0.23615532069219787614077375027971 absolute error = 4.69922181671802730992e-12 relative error = 1.9898860643285821699691384749992e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.39 y1(analytic)= = -0.96930522150296087116533607467248 y1(numeric) = = -0.96930522148777873448160345649268 absolute error = 1.518213668373261817980e-11 relative error = 1.5662906117633291148747756522995e-09 % glob_h = 0.01 y2(analytic)= = -0.24586050428463690513600137155794 y2(numeric) = = -0.24586050427977129430849289577521 absolute error = 4.86561082750847578273e-12 relative error = 1.9790127908773322219054568757007e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.4 y1(analytic)= = -0.96679819257946101428220153976569 y1(numeric) = = -0.96679819256428229587995114323121 absolute error = 1.517871840225039653448e-11 relative error = 1.5699986324708462564592529474659e-09 % glob_h = 0.01 y2(analytic)= = -0.25554110202683131924990242936374 y2(numeric) = = -0.25554110202179888305777145676258 absolute error = 5.03243619213097260116e-12 relative error = 1.9693255418467188804551825071946e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.41 y1(analytic)= = -0.96419448464236568623478364095296 y1(numeric) = = -0.96419448462719220896425641351375 absolute error = 1.517347727052722743921e-11 relative error = 1.5736946759403316431818162145744e-09 % glob_h = 0.01 y2(analytic)= = -0.26519614587177325875244430757411 y2(numeric) = = -0.26519614586657358052812092948496 absolute error = 5.19967822432337808915e-12 relative error = 1.9606914750704970175364196791666e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.42 y1(analytic)= = -0.96149435806029884717415014560141 y1(numeric) = = -0.96149435804513244254514544188957 absolute error = 1.516640462900470371184e-11 relative error = 1.5773784320067287073738873453702e-09 % glob_h = 0.01 y2(analytic)= = -0.2748246703231240725009433576662 y2(numeric) = = -0.27482467031775675539677614782155 absolute error = 5.36731710416720984465e-12 relative error = 1.9529968317096885611525556271221e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.43 y1(analytic)= = -0.95869808284366860579948964122556 y1(numeric) = = -0.95869808282851111376679855950105 absolute error = 1.515749203269108172451e-11 relative error = 1.5810495821303064584573338687389e-09 % glob_h = 0.01 y2(analytic)= = -0.28442571253646236904429691459137 y2(numeric) = = -0.28442571253092703616391771363679 absolute error = 5.53533288037920095458e-12 relative error = 1.9461436278091738569086473965698e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=91.5MB, alloc=4.4MB, time=5.04 x[1] = = 3.44 y1(analytic)= = -0.95580593861766640355516501297249 y1(numeric) = = -0.95580593860251967230224402205861 absolute error = 1.514673125292099091388e-11 relative error = 1.5847077990357476984745082477804e-09 % glob_h = 0.01 y2(analytic)= = -0.29399831241556765639445181056032 y2(numeric) = = -0.29399831240986395092182664802297 absolute error = 5.70370547262516253735e-12 relative error = 1.9400470110736399875930795510076e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.45 y1(analytic)= = -0.95281821459430472850678513994775 y1(numeric) = = -0.9528182145791706142276948623292 absolute error = 1.513411427909027761855e-11 relative error = 1.5883527463351600184369231207502e-09 % glob_h = 0.01 y2(analytic)= = -0.30354151270842916399808636621989 y2(numeric) = = -0.30354151270255674932423047886609 absolute error = 5.87241467385588735380e-12 relative error = 1.9346331318763352642252379526082e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.46 y1(analytic)= = -0.94973520954349615510160537578203 y1(numeric) = = -0.94973520952837652178123965721894 absolute error = 1.511963332036571856309e-11 relative error = 1.5919840781340713997475463492519e-09 % glob_h = 0.01 y2(analytic)= = -0.31305435910297024610631577597493 y2(numeric) = = -0.31305435909692880595365094786508 absolute error = 6.04144015266482810985e-12 relative error = 1.9298374154495225456068040265408e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.47 y1(analytic)= = -0.94655723176317660188518005352668 y1(numeric) = = -0.94655723174807332107781071137317 absolute error = 1.510328080736934215351e-11 relative error = 1.5956014386194135275295691915772e-09 % glob_h = 0.01 y2(analytic)= = -0.32253590032247879418185398715726 y2(numeric) = = -0.32253590031626803272618670617126 absolute error = 6.21076145566728098600e-12 relative error = 1.9256031497447630381533615240253e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.48 y1(analytic)= = -0.94328459904847579482359814738228 y1(numeric) = = -0.94328459903339074542976104875255 absolute error = 1.508504939383709862973e-11 relative error = 1.5992044616284328369598636406551e-09 % glob_h = 0.01 y2(analytic)= = -0.33198518822073411538191643544275 y2(numeric) = = -0.33198518821435375737201563357081 absolute error = 6.38035800990080187194e-12 relative error = 1.9218803236662945157649902205007e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.49 y1(analytic)= = -0.93991763865993801915927867276677 y1(numeric) = = -0.93991763864487308720102704973038 absolute error = 1.506493195825162303639e-11 relative error = 1.6027927701974015065265898390110e-09 % glob_h = 0.01 y2(analytic)= = -0.3414012778768207645082874807375 y2(numeric) = = -0.34140127787027055538304090098036 absolute error = 6.55020912524657975714e-12 relative error = 1.9186246653739611812182709373231e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.5 y1(analytic)= = -0.93645668729079633769865762667176 y1(numeric) = = -0.93645668727575341609320878874832 absolute error = 1.504292160544883792344e-11 relative error = 1.6063659760889276980448433689600e-09 % glob_h = 0.01 y2(analytic)= = -0.35078322768961984812036880004364 y2(numeric) = = -0.35078322768289955412349731131042 absolute error = 6.72029399687148873322e-12 relative error = 1.9157968415803910327840404103543e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.51 y1(analytic)= = -0.93290209103330354808266630575758 y1(numeric) = = -0.93290209101828453641446816008487 absolute error = 1.501901166819814567271e-11 relative error = 1.6099236792965859014331688340876e-09 % glob_h = 0.01 y2(analytic)= = -0.36013009947196835175953992341737 y2(numeric) = = -0.36013009946507776005184938631801 absolute error = 6.89059170769053709936e-12 relative error = 1.9133617872523548799147126580510e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.52 y1(analytic)= = -0.92925420534412324591621651227224 y1(numeric) = = -0.92925420532913005020746054890717 absolute error = 1.499319570875596336507e-11 relative error = 1.6134654675255038126498419282409e-09 % glob_h = 0.01 y2(analytic)= = -0.36944095854447707443057432143296 y2(numeric) = = -0.36944095853741599319972489230294 absolute error = 7.06108123084942913002e-12 relative error = 1.9112881415933593840274699323535e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.53 y1(analytic)= = -0.92551339500878445462153901468401 y1(numeric) = = -0.92551339499381898710114665852901 absolute error = 1.496546752039235615500e-11 relative error = 1.6169909156474512529103418798029e-09 % glob_h = 0.01 y2(analytic)= = -0.37871487382899778862484425400664 y2(numeric) = = -0.37871487382176604719261730184268 absolute error = 7.23174143222695216396e-12 relative error = 1.9095477711531132204479568416075e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.54 y1(analytic)= = -0.92168003410520337652276888612977 y1(numeric) = = -0.92168003409026755539387835792486 absolute error = 1.493582112889052820491e-11 relative error = 1.6204995851288786760044926882927e-09 % glob_h = 0.01 y2(analytic)= = -0.38795091794173027924720110048451 y2(numeric) = = -0.38795091793432772817424420167804 absolute error = 7.40255107295689880647e-12 relative error = 1.9081153647556911570845648543264e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.55 y1(analytic)= = -0.91775450596627591295627082271047 y1(numeric) = = -0.91775450595137166216225188936098 absolute error = 1.490425079401893334949e-11 relative error = 1.6239910234302472055434359115764e-09 % glob_h = 0.01 y2(analytic)= = -0.39714816728595995082022742343695 y2(numeric) = = -0.39714816727838646200825819223466 absolute error = 7.57348881196923120229e-12 relative error = 1.9069680879368294291708039834183e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.56 y1(analytic)= = -0.91373720314154469412352061310366 y1(numeric) = = -0.91373720312667394311254484229162 absolute error = 1.487075101097577081204e-11 relative error = 1.6274647633748782351760006071878e-09 % glob_h = 0.01 y2(analytic)= = -0.40630570214441672928242142268591 y2(numeric) = = -0.40630570213667219607387123115033 absolute error = 7.74453320855019153558e-12 relative error = 1.9060852869343894924851182949597e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.57 y1(analytic)= = -0.90962852735794445195161343603674 y1(numeric) = = -0.90962852734310913543980780155983 absolute error = 1.483531651180563447691e-11 relative error = 1.6309203224854276878700011777254e-09 % glob_h = 0.01 y2(analytic)= = -0.41542260677124602256709945606629 y2(numeric) = = -0.41542260676333035984217839591987 absolute error = 7.91566272492106014642e-12 relative error = 1.9054482341351848408021768178790e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.58 y1(analytic)= = -0.90542888947962966139140085454902 y1(numeric) = = -0.90542888946483171912461276711097 absolute error = 1.479794226678808743805e-11 relative error = 1.6343572022859572711071173733947e-09 % glob_h = 0.01 y2(analytic)= = -0.42449796948358254294260094834376 y2(numeric) = = -0.42449796947549568721376568842391 absolute error = 8.08685572883525991985e-12 relative error = 1.9050399083588594241158390258721e-09 % memory used=95.3MB, alloc=4.4MB, time=5.25 glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.59 y1(analytic)= = -0.90113870946688846735564983934783 y1(numeric) = = -0.90113870945212984386985190255829 absolute error = 1.475862348579793678954e-11 relative error = 1.6377748875674316103804948419443e-09 % glob_h = 0.01 y2(analytic)= = -0.43353088275271783380787293204403 y2(numeric) = = -0.43353088274445974331167942913856 absolute error = 8.25809049619350290547e-12 relative error = 1.9048448045404517123491333401861e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.6 y1(analytic)= = -0.89675841633414700587029172526594 y1(numeric) = = -0.8967584163194296502506547383641 absolute error = 1.471735561963698690184e-11 relative error = 1.6411728456143150349941629080412e-09 % glob_h = 0.01 y2(analytic)= = -0.44252044329485238426672734749269 y2(numeric) = = -0.44252044328642303905305067503167 absolute error = 8.42934521367667246102e-12 relative error = 1.9048487683223666236242361828084e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.61 y1(analytic)= = -0.89228844810706831897164969353841 y1(numeric) = = -0.89228844809239418461031264080271 absolute error = 1.467413436133705273570e-11 relative error = 1.6445505253897739729031811833091e-09 % glob_h = 0.01 y2(analytic)= = -0.45146575216142325634494018639253 y2(numeric) = = -0.45146575215282265836354405480679 absolute error = 8.60059798139613158574e-12 relative error = 1.9050388518332074581095968195437e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.62 y1(analytic)= = -0.887729251778750153422404272068 y1(numeric) = = -0.88772925176412119777497025398332 absolute error = 1.462895564743401808468e-11 relative error = 1.6479073566768092241561454841641e-09 % glob_h = 0.01 y2(analytic)= = -0.46036591482899819216274354079485 y2(numeric) = = -0.46036591482022636534718239527946 absolute error = 8.77182681556114551539e-12 relative error = 1.9054031875534094249125807822676e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.63 y1(analytic)= = -0.88308128326502602342992354439801 y1(numeric) = = -0.88308128325044420777071081739261 absolute error = 1.458181565921272700540e-11 relative error = 1.6512427491724455460000187552088e-09 % glob_h = 0.01 y2(analytic)= = -0.46922004128872721172690481453191 y2(numeric) = = -0.46922004127978420207574171043741 absolute error = 8.94300965116310409450e-12 relative error = 1.9059308776753981430954476210921e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.64 y1(analytic)= = -0.87834500735887400722343724413409 y1(numeric) = = -0.87834500734434129639951474404051 absolute error = 1.453271082392250009358e-11 relative error = 1.6545560915318925865016062940191e-09 % glob_h = 0.01 y2(analytic)= = -0.47802724613534275625715663887291 y2(numeric) = = -0.47802724612622863191248041195318 absolute error = 9.11412434467622691973e-12 relative error = 1.9066118967820854770897872902657e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.65 y1(analytic)= = -0.87352089768393783657240447452827 y1(numeric) = = -0.87352089766945619875644140383736 absolute error = 1.448163781596307069091e-11 relative error = 1.6578467503593596906035190282061e-09 % glob_h = 0.01 y2(analytic)= = -0.48678664865569947710681138829532 y2(numeric) = = -0.48678664864641432843003695653088 absolute error = 9.28514867677443176444e-12 relative error = 1.9074370060099465361447140693846e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.66 y1(analytic)= = -0.86860943664716492709839092015993 y1(numeric) = = -0.86860943663273633354035018059533 absolute error = 1.442859355804073956460e-11 relative error = 1.6611140691419557535196229555843e-09 % glob_h = 0.01 y2(analytic)= = -0.49549737291684481637245114641035 y2(numeric) = = -0.49549737290738875601738710206348 absolute error = 9.45606035506404434687e-12 relative error = 1.9083976771459040489493278168740e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.67 y1(analytic)= = -0.86361111539056608553795618647981 y1(numeric) = = -0.86361111537619251031566163639397 absolute error = 1.437357522229455008584e-11 relative error = 1.6643573671228322099242277208313e-09 % glob_h = 0.01 y2(analytic)= = -0.50415854785361157220802405891391 y2(numeric) = = -0.50415854784398473519119203381994 absolute error = 9.62683701683202509397e-12 relative error = 1.9094860253420302347775901143037e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.68 y1(analytic)= = -0.85852643374210171794562486853616 y1(numeric) = = -0.85852643372778513771423257908947 absolute error = 1.431658023139228944669e-11 relative error = 1.6675759381094303198853339772154e-09 % glob_h = 0.01 y2(analytic)= = -0.51276930735572368965980922504404 y2(numeric) = = -0.51276930734592623342799983886362 absolute error = 9.79745623180938618042e-12 relative error = 1.9106947493276137762230704968953e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.69 y1(analytic)= = -0.85335590016569945017519302837216 y1(numeric) = = -0.85335590015144184391559690337732 absolute error = 1.425760625959612499484e-11 relative error = 1.6707690492123708134669018326006e-09 % glob_h = 0.01 y2(analytic)= = -0.52132879035440656651575454812466 y2(numeric) = = -0.52132879034443867101080507833719 absolute error = 9.96789550494946978747e-12 relative error = 1.9120170781615869918794756317676e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.7 y1(analytic)= = -0.8481000317104081588356701063544 y1(numeric) = = -0.8481000316962115076018724180205 absolute error = 1.419665123379768833390e-11 relative error = 1.6739359395101721020851147570514e-09 % glob_h = 0.01 y2(analytic)= = -0.52983614090849321321077762570121 y2(numeric) = = -0.52983614089835508093155686947184 absolute error = 1.013813227922075622937e-11 relative error = 1.9134467237054125084978815664329e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.71 y1(analytic)= = -0.84275935395869349727638917260975 y1(numeric) = = -0.84275935394455978394186674917883 absolute error = 1.413371333452242343092e-11 relative error = 1.6770758186345997886866906898300e-09 % glob_h = 0.01 y2(analytic)= = -0.53829050829001765624379404325037 y2(numeric) = = -0.53829050827970951230538017491298 absolute error = 1.030814393841386833739e-11 relative error = 1.9149778381119242202408891113271e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.72 y1(analytic)= = -0.83733440097388008700560008948967 y1(numeric) = = -0.83733440095981129600869707089568 absolute error = 1.406879099690301859399e-11 relative error = 1.6801878652710319258149360006021e-09 % glob_h = 0.01 y2(analytic)= = -0.54669104706928702583745896705622 y2(numeric) = = -0.54669104705880911802749653078467 absolute error = 1.047790780996243627155e-11 relative error = 1.9166049757230572840931746841956e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=5.46 NO POLE NO POLE x[1] = = 3.73 y1(analytic)= = -0.83182571524674563027960569792163 y1(numeric) = = -0.83182571523274374736798395209189 absolute error = 1.400188291162174582974e-11 relative error = 1.6832712255677678388311868804123e-09 % glob_h = 0.01 y2(analytic)= = -0.55503691719942382070274923216573 y2(numeric) = = -0.55503691718877641953497174741551 absolute error = 1.064740116777748475022e-11 relative error = 1.9183230588519378816086240198558e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.74 y1(analytic)= = -0.82623384764127228440667735620253 y1(numeric) = = -0.82623384762733929638085582143998 absolute error = 1.393298802582153476255e-11 relative error = 1.6863250114477094084863979721444e-09 % glob_h = 0.01 y2(analytic)= = -0.56332728410036989575236111967948 y2(numeric) = = -0.56332728408955329451726611713268 absolute error = 1.081660123509500254680e-11 relative error = 1.9201273469949260846219931052398e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.75 y1(analytic)= = -0.82055935733956072258311240229071 y1(numeric) = = -0.82055935732569861703912679029523 absolute error = 1.386210554398561199548e-11 relative error = 1.6893482988152980997665056030433e-09 % glob_h = 0.01 y2(analytic)= = -0.57156131874234377243415557335029 y2(numeric) = = -0.57156131873135828724681922134894 absolute error = 1.098548518733635200135e-11 relative error = 1.9220134090789547017076073145167e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.76 y1(analytic)= = -0.81480281178591238980944513756309 y1(numeric) = = -0.81480281177212315488065959704848 absolute error = 1.378923492878554051461e-11 relative error = 1.6923401256509938316108862463943e-09 % glob_h = 0.01 y2(analytic)= = -0.57973819772874292602316503775395 y2(numeric) = = -0.57973819771758889586818386352002 absolute error = 1.115403015498117423393e-11 relative error = 1.9239770984005608364339263536467e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.77 y1(analytic)= = -0.80896478663008554561462174619622 y1(numeric) = = -0.80896478661637116971272424871053 absolute error = 1.371437590189749748569e-11 relative error = 1.6952994899849275323606693569069e-09 % glob_h = 0.01 y2(analytic)= = -0.58785710337848275971251772647441 y2(numeric) = = -0.5878571033671605464860652827491 absolute error = 1.132221322645244372531e-11 relative error = 1.9260145299567488223180694663097e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.78 y1(analytic)= = -0.80304586566973076793658025923771 y1(numeric) = = -0.80304586565609323949179362667601 absolute error = 1.363752844478663256170e-11 relative error = 1.6982253477406417999528506554409e-09 % glob_h = 0.01 y2(analytic)= = -0.59591722380776403167448581090021 y2(numeric) = = -0.59591722379627402022347248694976 absolute error = 1.149001145101332395045e-11 relative error = 1.9281220599053985495822811918258e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.79 y1(analytic)= = -0.79704664079201167456087725184016 y1(numeric) = = -0.79704664077845298176141789922551 absolute error = 1.355869279945935261465e-11 relative error = 1.7011166104390466362267673434459e-09 % glob_h = 0.01 y2(analytic)= = -0.60391775301126055841709072023268 y2(numeric) = = -0.60391775299960315657541524642241 absolute error = 1.165740184167547381027e-11 relative error = 1.9302962669252929995435911556608e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.8 y1(analytic)= = -0.79096771191441669999656817435073 y1(numeric) = = -0.79096771190093883052738479173006 absolute error = 1.347786946918338262067e-11 relative error = 1.7039721427518520770638262376658e-09 % glob_h = 0.01 y2(analytic)= = -0.61185789094271907573358608611888 y2(numeric) = = -0.61185789093089471435546763340992 absolute error = 1.182436137811845270896e-11 relative error = 1.9325339352737751990268798637965e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.81 y1(analytic)= = -0.78480968692476784656233037436496 y1(numeric) = = -0.78480968691137278734315491809697 absolute error = 1.339505921917545626799e-11 relative error = 1.7067907598927880857480432320189e-09 % glob_h = 0.01 y2(analytic)= = -0.61973684359496319732588971051781 y2(numeric) = = -0.61973684358297233031626984025127 absolute error = 1.199086700961987026654e-11 relative error = 1.9348320393642195808992627819760e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.82 y1(analytic)= = -0.7785731816204324087577276566562 y1(numeric) = = -0.77857318160712214568047116293838 absolute error = 1.331026307725649371782e-11 relative error = 1.7095712248338746448748025344967e-09 % glob_h = 0.01 y2(analytic)= = -0.62755382307929347077277195688991 y2(numeric) = = -0.62755382306713657511477603204876 absolute error = 1.215689565799592484115e-11 relative error = 1.9371877297064703651532810924274e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.83 y1(analytic)= = -0.77225881964674374969652252702348 y1(numeric) = = -0.77225881963352026736204839919165 absolute error = 1.322348233447412783183e-11 relative error = 1.7123122453328506967625323231771e-09 % glob_h = 0.01 y2(analytic)= = -0.63530804770427559090337023862228 y2(numeric) = = -0.6353080476919531666828182653606 absolute error = 1.232242422055197326168e-11 relative error = 1.9395983200716259354800387170226e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.84 y1(analytic)= = -0.76586723243463728747307694024768 y1(numeric) = = -0.76586723242150256892738449616376 absolute error = 1.313471854569244408392e-11 relative error = 1.7150124707565971958437998628129e-09 % glob_h = 0.01 y2(analytic)= = -0.64299874205390889182034887886274 y2(numeric) = = -0.64299874204142146224730610642333 absolute error = 1.248742957304277243941e-11 relative error = 1.9420612757584257804312318421612e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.85 y1(analytic)= = -0.75939905913750792781123507395279 y1(numeric) = = -0.75939905912446395428108627065382 absolute error = 1.304397353014880329897e-11 relative error = 1.7176704886839832393518332773440e-09 % glob_h = 0.01 y2(analytic)= = -0.650625137065167300788642218662 y2(numeric) = = -0.65062513705251541221600018682324 absolute error = 1.265188857264203183876e-11 relative error = 1.9445742028523569508088131018356e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.86 y1(analytic)= = -0.75285494656729525719980460936484 y1(numeric) = = -0.75285494655434400782782698905807 absolute error = 1.295124937197762030677e-11 relative error = 1.7202848212700094428784028869218e-09 % glob_h = 0.01 y2(analytic)= = -0.6581864701049049999590093452957 y2(numeric) = = -0.65818647009208922189808843115583 absolute error = 1.281577806092091413987e-11 relative error = 1.9471348383807209434835158511336e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE memory used=103.0MB, alloc=4.4MB, time=5.67 NO POLE x[1] = = 3.87 y1(analytic)= = -0.74623554912980288794206080932728 y1(numeric) = = -0.74623554911694633952135983376339 absolute error = 1.285654842070097556389e-11 relative error = 1.7228539213514017969884786951538e-09 % glob_h = 0.01 y2(analytic)= = -0.66568198504611910542431592310351 y2(numeric) = = -0.665681985033140030557480803281 absolute error = 1.297907486683511982251e-11 relative error = 1.9497410412775278417940154856097e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.88 y1(analytic)= = -0.73954152875925842313086807704128 y1(numeric) = = -0.73954152874649854983918213625997 absolute error = 1.275987329168594078131e-11 relative error = 1.7253761682719022227799710820395e-09 % glob_h = 0.01 y2(analytic)= = -0.67311093234356173740418951936854 y2(numeric) = = -0.67311093233041998159446932952894 absolute error = 1.314175580972018983960e-11 relative error = 1.9523907840814152964745803871261e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.89 y1(analytic)= = -0.73277355485212058549838830263169 y1(numeric) = = -0.73277355483945935863181979903333 absolute error = 1.266122686656850359836e-11 relative error = 1.7278498634033863107720672534805e-09 % glob_h = 0.01 y2(analytic)= = -0.68047256910869392041403980815868 y2(numeric) = = -0.68047256909539012271174514912719 absolute error = 1.330379770229465903149e-11 relative error = 1.9550821452979985737603908181785e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.9 y1(analytic)= = -0.72593230420014012937233048461435 y1(numeric) = = -0.72593230418757951707868650424873 absolute error = 1.256061229364398036562e-11 relative error = 1.7302732253365885882847495143513e-09 % glob_h = 0.01 y2(analytic)= = -0.68776615918397381809088812537869 y2(numeric) = = -0.68776615917050864073721743392053 absolute error = 1.346517735367069145816e-11 relative error = 1.9578133023652923834403529421672e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.91 y1(analytic)= = -0.71901846092268122959176361387439 y1(numeric) = = -0.71901846091022319660353980373532 absolute error = 1.245803298822381013907e-11 relative error = 1.7326443847126019025646598309829e-09 % glob_h = 0.01 y2(analytic)= = -0.69499097321647187391443044807649 y2(numeric) = = -0.6949909732028460023420586206805 absolute error = 1.362587157237182739599e-11 relative error = 1.9605825251672323036232633600393e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.92 y1(analytic)= = -0.71203271639831011518720258429259 y1(numeric) = = -0.71203271638595662255424395724792 absolute error = 1.235349263295862704467e-11 relative error = 1.7349613786634068621732131374457e-09 % glob_h = 0.01 y2(analytic)= = -0.70214628873080549637060743782065 y2(numeric) = = -0.70214628871701963920124996746052 absolute error = 1.378585716935747036013e-11 relative error = 1.9633881700459722003605816743493e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.93 y1(analytic)= = -0.70497576919565778890458983952695 y1(numeric) = = -0.70497576918341079372646232727989 absolute error = 1.224699517812751224706e-11 relative error = 1.7372221448264418021623793595478e-09 % glob_h = 0.01 y2(analytic)= = -0.70923139020138599514994389285155 y2(numeric) = = -0.70923139018744088418889015168091 absolute error = 1.394511096105374117064e-11 relative error = 1.9662286742686377696904468706611e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.94 y1(analytic)= = -0.69784832500356374624360614943559 y1(numeric) = = -0.69784832499142520140171281858913 absolute error = 1.213854484189333084646e-11 relative error = 1.7394245148946000795588467167812e-09 % glob_h = 0.01 y2(analytic)= = -0.71624556912397054374724335454079 y2(numeric) = = -0.71624556910986693397485302975741 absolute error = 1.410360977239032478338e-11 relative error = 1.9691025509086559730015865271635e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.95 y1(analytic)= = -0.69065109656050767958019331164023 y1(numeric) = = -0.69065109654847953346966924850543 absolute error = 1.202814611052406313480e-11 relative error = 1.7415662076589900605757996106911e-09 % glob_h = 0.01 y2(analytic)= = -0.72318812408651201332600433544282 y2(numeric) = = -0.72318812407225068288616140108967 absolute error = 1.426133043984293435315e-11 relative error = 1.9720083841057254691730159026898e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.96 y1(analytic)= = -0.68338480358333622414406980875151 y1(numeric) = = -0.6833848035714204204054897649874 absolute error = 1.191580373858004376411e-11 relative error = 1.7436448214972570731726228577174e-09 % glob_h = 0.01 y2(analytic)= = -0.73005836083929959292321305873169 y2(numeric) = = -0.73005836082488134310873204294337 absolute error = 1.441824981448101578832e-11 relative error = 1.9749448246720045660993186646598e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.97 y1(analytic)= = -0.67605017269529187311724748931934 y1(numeric) = = -0.67605017268349035036818046280143 absolute error = 1.180152274906702651791e-11 relative error = 1.7456578262551805873251858534345e-09 % glob_h = 0.01 y2(analytic)= = -0.73685559236438318199094255175134 y2(numeric) = = -0.7368555923498088372259222368592 absolute error = 1.457434476502031489214e-11 relative error = 1.9779105860152230970491204879540e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.98 y1(analytic)= = -0.66864793735335125890206371667484 y1(numeric) = = -0.6686479373416659504685087201469 absolute error = 1.168530843355499652794e-11 relative error = 1.7476025544635488647500943952606e-09 % glob_h = 0.01 y2(analytic)= = -0.7435791389442746128933574013766 y2(numeric) = = -0.74357913892954502071247747330823 absolute error = 1.472959218087992806837e-11 relative error = 1.9809044403522184793257017236100e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 3.99 y1(analytic)= = -0.66117883777488006667005095201013 y1(numeric) = = -0.66117883776331290031778829606532 absolute error = 1.156716635226265594481e-11 relative error = 1.7494761918258907707919981582349e-09 % glob_h = 0.01 y2(analytic)= = -0.75022832822991883329412529862008 y2(numeric) = = -0.75022832821503486431888184212546 absolute error = 1.488396897524345649462e-11 relative error = 1.9839252151888936385816840332625e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4 y1(analytic)= = -0.65364362086361191463916818309775 y1(numeric) = = -0.653643620852164812305060669847 absolute error = 1.144710233410751325075e-11 relative error = 1.7512757669054104849315913832625e-09 % glob_h = 0.01 y2(analytic)= = -0.75680249530792825137263909451183 y2(numeric) = = -0.75680249529289079928451521187174 absolute error = 1.503745208812388264009e-11 relative error = 1.9869717900448300123187793058895e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=106.8MB, alloc=4.4MB, time=5.87 x[1] = = 4.01 y1(analytic)= = -0.64604304013495860312968241468503 y1(numeric) = = -0.64604304012363348065296090408951 absolute error = 1.132512247672151059552e-11 relative error = 1.7529981399313099624104593090090e-09 % glob_h = 0.01 y2(analytic)= = -0.7633009827670735204905561792977 y2(numeric) = = -0.76330098275188350200112439227623 absolute error = 1.519001848943178702147e-11 relative error = 1.9900430934027926359494754827588e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.02 y1(analytic)= = -0.63837785564065920131155338076535 y1(numeric) = = -0.63837785562945796816512125302371 absolute error = 1.120123314643212774164e-11 relative error = 1.7546399906354623143595311750096e-09 % glob_h = 0.01 y2(analytic)= = -0.76972314076402411428559733354449 y2(numeric) = = -0.76972314074868246910355081138946 absolute error = 1.534164518204652215503e-11 relative error = 1.9931380998651627442363764562951e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.03 y1(analytic)= = -0.63064883389277550667185452185245 y1(numeric) = = -0.63064883388170006569364561642944 absolute error = 1.107544097820890542301e-11 relative error = 1.7561978050199613341840676064541e-09 % glob_h = 0.01 y2(analytic)= = -0.7760683270883321181898793012325 y2(numeric) = = -0.77606832707283980898498934146029 absolute error = 1.549230920488995977221e-11 relative error = 1.9962558275009495027735500173321e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.04 y1(analytic)= = -0.62285674778704147759294657917268 y1(numeric) = = -0.62285674777609372471737124402288 absolute error = 1.094775287557533514980e-11 relative error = 1.7576678609442373184805746364595e-09 % glob_h = 0.01 y2(analytic)= = -0.78233590722665273904778223066649 y2(numeric) = = -0.78233590721101075141177980414483 absolute error = 1.564198763600242652166e-11 relative error = 1.9993953353684867016660828603310e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.05 y1(analytic)= = -0.61500237652557430403427072848237 y1(numeric) = = -0.61500237651475612802378466174936 absolute error = 1.081817601048606673301e-11 relative error = 1.7590462124069861877266605462913e-09 % glob_h = 0.01 y2(analytic)= = -0.78852525442619511083590710941938 y2(numeric) = = -0.78852525441040445324028666683648 absolute error = 1.579065759562044258290e-11 relative error = 2.0025557212002303235528179302528e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.06 y1(analytic)= = -0.60708650553895484514628584778934 y1(numeric) = = -0.60708650552826812732311645873647 absolute error = 1.068671782316938905287e-11 relative error = 1.7603286723828612172104337581914e-09 % glob_h = 0.01 y2(analytic)= = -0.79463574975739705145742669274634 y2(numeric) = = -0.79463574974145875520817081588183 absolute error = 1.593829624925587686451e-11 relative error = 2.0057361192372545319994681092338e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.07 y1(analytic)= = -0.59910992640768522570785577303961 y1(numeric) = = -0.5991099263971318396859208291833 absolute error = 1.055338602193494385631e-11 relative error = 1.7615107940564357465999949817305e-09 % glob_h = 0.01 y2(analytic)= = -0.80066678217581750318737928027569 y2(numeric) = = -0.80066678215973262237660314852072 absolute error = 1.608488081077613175497e-11 relative error = 2.0089356982021106465424843759110e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.08 y1(analytic)= = -0.59107343678303144556199101824792 y1(numeric) = = -0.59107343677261325697904438160854 absolute error = 1.041818858294663663938e-11 relative error = 1.7625878502760221347629031297502e-09 % glob_h = 0.01 y2(analytic)= = -0.80661774858324046757643767338011 y2(numeric) = = -0.80661774856701007903095270364476 absolute error = 1.623038854548496973535e-11 relative error = 2.0121536593996782877520958315116e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.09 y1(analytic)= = -0.58297784030725891772303711364428 y1(numeric) = = -0.58297784029697778397307640069408 absolute error = 1.028113374996071295020e-11 relative error = 1.7635548110271281536851372696430e-09 % glob_h = 0.01 y2(analytic)= = -0.81248805388798432447058271235272 y2(numeric) = = -0.81248805387160952769737911880156 absolute error = 1.637479677320359355116e-11 relative error = 2.0153892349365108840383378130677e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.1 y1(analytic)= = -0.57482394653326891153502867965979 y1(numeric) = = -0.57482394652312668150099970692319 absolute error = 1.014223003402897273660e-11 relative error = 1.7644063186991765241835683986534e-09 % glob_h = 0.01 y2(analytic)= = -0.81827711106441050426503702435845 y2(numeric) = = -0.81827711104789242139368543328283 absolute error = 1.651808287135159107562e-11 relative error = 2.0186416860499686867485860324715e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.11 y1(analytic)= = -0.56661257084364393716992399387447 y1(numeric) = = -0.56661257083364245095675689421578 absolute error = 1.000148621316709965869e-11 relative error = 1.7651366608890500322532358211668e-09 % glob_h = 0.01 y2(analytic)= = -0.82398434121162556257482398369604 y2(numeric) = = -0.82398434119496533829679662821741 absolute error = 1.666022427802735547863e-11 relative error = 2.0219103015391498111296576472328e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.12 y1(analytic)= = -0.5583445343691101668598082727593 y1(numeric) = = -0.55834453435925125552782018616832 absolute error = 9.85891133198808659098e-12 relative error = 1.7657397404503939656537598202637e-09 % glob_h = 0.01 y2(analytic)= = -0.82960917361137078716340306097222 y2(numeric) = = -0.82960917359456958866831547012781 absolute error = 1.680119849508759084441e-11 relative error = 2.0251943962902811252089397818316e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.13 y1(analytic)= = -0.55002066390642504655299469207052 y1(numeric) = = -0.55002066389671053185169394922097 absolute error = 9.71451470130074284955e-12 relative error = 1.7662090424576252172966579690027e-09 % glob_h = 0.01 y2(analytic)= = -0.83515104578509354821692987595635 y2(numeric) = = -0.83515104576815256512570436299912 absolute error = 1.694098309122551295723e-11 relative error = 2.0284933098898227272496495336120e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.14 y1(analytic)= = -0.54164179183569830916443077359731 y1(numeric) = = -0.5416417918261300032667575005996 absolute error = 9.56830589767327299771e-12 relative error = 1.7665375977073283407180637673033e-09 % glob_h = 0.01 y2(analytic)= = -0.84060940355019468487667282814088 y2(numeric) = = -0.84060940353311512917162547354307 absolute error = 1.707955570504735459781e-11 relative error = 2.0318064053190782293403210561648e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.15 y1(analytic)= = -0.53320875603715465725018617166272 memory used=110.6MB, alloc=4.4MB, time=6.07 y1(numeric) = = -0.53320875602773436248722425025589 absolute error = 9.42029476296192140683e-12 relative error = 1.7667179423260452629891201705787e-09 % glob_h = 0.01 y2(analytic)= = -0.84598370107544630333780572921222 y2(numeric) = = -0.84598370105822940928965894484848 absolute error = 1.721689404814678436374e-11 relative error = 2.0351330677245933956990634694624e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.16 y1(analytic)= = -0.52472239980734643876839021070922 y1(numeric) = = -0.52472239979807594736458552963031 absolute error = 9.27049140380468107891e-12 relative error = 1.7667420729910468088086993200429e-09 % glob_h = 0.01 y2(analytic)= = -0.85127340093557444478094790264673 y2(numeric) = = -0.8512734009182214688727710549011 absolute error = 1.735297590817684774563e-11 relative error = 2.0384727032590725929064331021305e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.17 y1(analytic)= = -0.51618357177482469458922054275779 y1(numeric) = = -0.51618357176570578839814047318679 absolute error = 9.11890619108006957100e-12 relative error = 1.7666013971978983597973677310882e-09 % glob_h = 0.01 y2(analytic)= = -0.85647797416500116491514400141294 y2(numeric) = = -0.85647797414751338576322496245684 absolute error = 1.748777915191903895610e-11 relative error = 2.0418247379879502135211121446642e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.18 y1(analytic)= = -0.50759312581527701057891803304672 y1(numeric) = = -0.5075931258063114608195870538457 absolute error = 8.96554975933097920102e-12 relative error = 1.7662866779235534316961387927612e-09 % glob_h = 0.01 y2(analytic)= = -0.86159690031074065096911416280091 y2(numeric) = = -0.86159690029311936924076505097872 absolute error = 1.762128172834911182219e-11 relative error = 2.0451886168571265055180610542443e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.19 y1(analytic)= = -0.49895192096614066040190125149245 y1(numeric) = = -0.49895192095733022739574763843577 absolute error = 8.81043300615361305668e-12 relative error = 1.7657879719339726126997924524546e-09 % glob_h = 0.01 y2(analytic)= = -0.86662966748444408656315532592254 y2(numeric) = = -0.86662966746669062489145608800988 absolute error = 1.775346167169923791266e-11 relative error = 2.0485638027177174527675977155247e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.2 y1(analytic)= = -0.49026082134069957765554488137713 y1(numeric) = = -0.49026082133204601056399335870143 absolute error = 8.65356709155152267570e-12 relative error = 1.7650945608680104914199728968716e-09 % glob_h = 0.01 y2(analytic)= = -0.87157577241358806001857709790882 y2(numeric) = = -0.87157577239570376291406097792868 absolute error = 1.788429710451611998014e-11 relative error = 2.0519497754039795304786341833146e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.21 y1(analytic)= = -0.48152069604167374756882294948685 y1(numeric) = = -0.48152069603317878413156818187216 absolute error = 8.49496343725476761469e-12 relative error = 1.7641948740910528789066172881815e-09 % glob_h = 0.01 y2(analytic)= = -0.8764347204918013973064980899522 y2(numeric) = = -0.87643472047378763106578342119759 absolute error = 1.801376624071466875461e-11 relative error = 2.0553460308608550167150689300800e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.22 y1(analytic)= = -0.47273241907430965925363841315521 y1(numeric) = = -0.47273241906597502552763419168002 absolute error = 8.33463372600422147519e-12 relative error = 1.7630764021483547563452063348603e-09 % glob_h = 0.01 y2(analytic)= = -0.88120602582832538699464673122123 y2(numeric) = = -0.88120602581018353960601988009244 absolute error = 1.814184738862685112879e-11 relative error = 2.0587520803178445122679312305027e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.23 y1(analytic)= = -0.46389686925898050939118958954484 y1(numeric) = = -0.46389686925080791949038853623547 absolute error = 8.17258990080105330937e-12 relative error = 1.7617255994539871270028071209688e-09 % glob_h = 0.01 y2(analytic)= = -0.88588921129660245121088859729926 y2(numeric) = = -0.88588921127833393225684327947108 absolute error = 1.826851895404531782818e-11 relative error = 2.0621674495061525955158842088748e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.24 y1(analytic)= = -0.45501493014330489726017186970594 y1(numeric) = = -0.45501493013529605309605045202366 absolute error = 8.00884416412141768228e-12 relative error = 1.7601277746202895766986469082602e-09 % glob_h = 0.01 y2(analytic)= = -0.89048380858198840379687432458221 y2(numeric) = = -0.89048380856359464435361290582397 absolute error = 1.839375944326141875824e-11 relative error = 2.0655916779162720859910363106327e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.25 y1(analytic)= = -0.44608748991379279916407772054484 y1(numeric) = = -0.44608748990594939018698132952167 absolute error = 7.84340897709639102317e-12 relative error = 1.7582669665567496094233119057078e-09 % glob_h = 0.01 y2(analytic)= = -0.89498935822858352446575282843828 y2(numeric) = = -0.894989358210065976999655614069 absolute error = 1.851754746609721436928e-11 relative error = 2.0690243180933739841103961879763e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.26 y1(analytic)= = -0.43711544130702765758652413548598 y1(numeric) = = -0.4371154412993513605278669392312 absolute error = 7.67629705865719625478e-12 relative error = 1.7561258041363504095632376806042e-09 % glob_h = 0.01 y2(analytic)= = -0.89940540968517776589555981885312 y2(numeric) = = -0.89940540966653790415662872727782 absolute error = 1.863986173893109157530e-11 relative error = 2.0724649349680553939071330813701e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.27 y1(analytic)= = -0.42809968152039346679167732209429 y1(numeric) = = -0.42809968151288594540703156004947 absolute error = 7.50752138464576204482e-12 relative error = 1.7536853468292348650074547457954e-09 % glob_h = 0.01 y2(analytic)= = -0.90373152135030549927585981966133 y2(numeric) = = -0.90373152133154481818814322665449 absolute error = 1.876068108771659300684e-11 relative error = 2.0759131052201680635045023585180e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.28 y1(analytic)= = -0.41904111212235578208682073683604 y1(numeric) = = -0.41904111211501868689993006945691 absolute error = 7.33709518689066737913e-12 relative error = 1.7509249032224574470963252618909e-09 % glob_h = 0.01 y2(analytic)= = -0.90796726061640529287063252329942 y2(numeric) = = -0.90796726059752530841963845462971 absolute error = 1.887998445099406866971e-11 relative error = 2.0793684166736068975717933927831e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.29 y1(analytic)= = -0.40994063896230562457137463377925 y1(numeric) = = -0.40994063895514059261912610726931 absolute error = 7.16503195224852650994e-12 relative error = 1.7478218237610145868001936824651e-09 % glob_h = 0.01 y2(analytic)= = -0.91211220391308030765634688524802 y2(numeric) = = -0.91211220389408255677345212582676 absolute error = 1.899775088289475942126e-11 relative error = 2.0828304677200820849714413587353e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=6.26 NO POLE NO POLE x[1] = = 4.3 y1(analytic)= = -0.40079917207997529690676239633603 y1(numeric) = = -0.40079917207298395148515152265164 absolute error = 6.99134542161087368439e-12 relative error = 1.7443512633344021934360311153637e-09 % glob_h = 0.01 y2(analytic)= = -0.91616593674945498403170936028464 y2(numeric) = = -0.91616593673034102447557243822115 absolute error = 1.911395955613692206349e-11 relative error = 2.0862988667700314088827820993646e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.31 y1(analytic)= = -0.39161762561443516845006009684425 y1(numeric) = = -0.39161762560761911886118348543569 absolute error = 6.81604958887661140856e-12 relative error = 1.7404859084629947094556430329039e-09 % glob_h = 0.01 y2(analytic)= = -0.92012805375562378396571242699099 y2(numeric) = = -0.92012805373639519420069882070276 absolute error = 1.922858976501360628823e-11 relative error = 2.0897732317289518308314351627410e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.32 y1(analytic)= = -0.38239691771268052999708015943008 y1(numeric) = = -0.38239691770604137129719006908126 absolute error = 6.63915869989009034882e-12 relative error = 1.7361956627690494423131606743302e-09 % glob_h = 0.01 y2(analytic)= = -0.92399815872318784374430909898398 y2(numeric) = = -0.92399815870384622281593740479054 absolute error = 1.934162092837169419344e-11 relative error = 2.0932531894975424386293794263023e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.33 y1(analytic)= = -0.37313797043781765937323745066286 y1(numeric) = = -0.37313797043135697212189255734653 absolute error = 6.46068725134489331633e-12 relative error = 1.7314472830959313382655431693429e-09 % glob_h = 0.01 y2(analytic)= = -0.92777586464487548368421918677298 y2(numeric) = = -0.92777586462542245109163737315197 absolute error = 1.945303259258181362101e-11 relative error = 2.0967383754941551142194217836265e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.34 y1(analytic)= = -0.36384170967685827918912735442367 y1(numeric) = = -0.36384170967057762919947395430388 absolute error = 6.28064998965340011979e-12 relative error = 1.7262039569986314353955608033384e-09 % glob_h = 0.01 y2(analytic)= = -0.93146079375324261279591291098884 y2(numeric) = = -0.93146079373367980836141417384204 absolute error = 1.956280443449873714680e-11 relative error = 2.1002284331981455307368609994338e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.35 y1(analytic)= = -0.35450906504813162723820257743587 y1(numeric) = = -0.35450906504203256532842036302868 absolute error = 6.09906190978221440719e-12 relative error = 1.7204248102807035274520096924055e-09 % glob_h = 0.01 y2(analytic)= = -0.93505257755844915838755579834142 y2(numeric) = = -0.93505257753877824212314391916075 absolute error = 1.967091626441187918067e-11 relative error = 2.1037230137128059822229130045396e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.36 y1(analytic)= = -0.34514096980832339825235256696343 y1(numeric) = = -0.34514096980240745999829902901593 absolute error = 5.91593825405353794750e-12 relative error = 1.7140643306817496075065605059686e-09 % glob_h = 0.01 y2(analytic)= = -0.93855085688510774299843471888496 y2(numeric) = = -0.93855085686533039496944921457477 absolute error = 1.977734802898550431019e-11 relative error = 2.1072217753466436787787422414338e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.37 y1(analytic)= = -0.33573836075915085304374269242283 y1(numeric) = = -0.33573836075341955853283011029446 absolute error = 5.73129451091258212837e-12 relative error = 1.7070716905727819803845130747157e-09 % glob_h = 0.01 y2(analytic)= = -0.94195528190820092382487885040826 y2(numeric) = = -0.94195528188831884401069058966324 absolute error = 1.988207981418826074502e-11 relative error = 2.1107243832118440447804078198548e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.38 y1(analytic)= = -0.32630217815368342744422852384408 y1(numeric) = = -0.32630217814813828103056741307932 absolute error = 5.54514641366111076476e-12 relative error = 1.6993899473908599065394698447928e-09 % glob_h = 0.01 y2(analytic)= = -0.94526551218806340294466391093816 y2(numeric) = = -0.94526551216807831109645225744811 absolute error = 1.998509184821165349005e-11 relative error = 2.1142305088388287299572414086387e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.39 y1(analytic)= = -0.31683336560231820890338536675574 y1(numeric) = = -0.31683336559696069896422815412986 absolute error = 5.35750993915721262588e-12 relative error = 1.6909550952666497679969347315158e-09 % glob_h = 0.01 y2(analytic)= = -0.94848121670442571014802896361413 y2(numeric) = = -0.94848121668433934564365189091949 absolute error = 2.008636450437707269464e-11 relative error = 2.1177398298058829305737404526978e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.4 y1(analytic)= = -0.30733286997841968311913974221771 y1(numeric) = = -0.30733286997325128181265833582416 absolute error = 5.16840130648140639355e-12 relative error = 1.6816949345002770088941463158645e-09 % glob_h = 0.01 y2(analytic)= = -0.95160207388951595403539233338039 y2(numeric) = = -0.95160207386933007573136133988849 absolute error = 2.018587830403099349190e-11 relative error = 2.1212520293828866286254606659065e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.41 y1(analytic)= = -0.29780164132363318664770646649064 y1(numeric) = = -0.29780164131865534967213728142795 absolute error = 4.97783697556918506269e-12 relative error = 1.6715277167191857909782475782342e-09 % glob_h = 0.01 y2(analytic)= = -0.95462777166021633123424156453615 y2(numeric) = = -0.95462777163993271731481359997983 absolute error = 2.028361391942796455632e-11 relative error = 2.1247667961882398628902519050654e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.42 y1(analytic)= = -0.28824063275288153406866514349322 y1(numeric) = = -0.28824063274809570042285503240854 absolute error = 4.78583364581011108468e-12 relative error = 1.6603605120146847966783176736248e-09 % glob_h = 0.01 y2(analytic)= = -0.95755800744927117811107273183889 y2(numeric) = = -0.95755800742889162593447172826866 absolute error = 2.037955217660100357023e-11 relative error = 2.1282838238581234861143216967320e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.43 y1(analytic)= = -0.27865080035905431996329034893364 y1(numeric) = = -0.27865080035446191170867677109786 absolute error = 4.59240825461357783578e-12 relative error = 1.6480872291398587202297806050457e-09 % glob_h = 0.01 y2(analytic)= = -0.96039248823554344419921453430048 y2(numeric) = = -0.96039248821506977014099551550156 absolute error = 2.047367405821901879892e-11 relative error = 2.1318028107272843470009827856761e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.4MB, time=6.47 NO POLE x[1] = = 4.44 y1(analytic)= = -0.26903310311739942669651235616339 y1(numeric) = = -0.26903310311300184872057099889874 absolute error = 4.39757797594135726465e-12 relative error = 1.6345861996106711215559086853768e-09 % glob_h = 0.01 y2(analytic)= = -0.96313093057331656172040803307784 y2(numeric) = = -0.96313093055275060101397715604644 absolute error = 2.056596070643087703140e-11 relative error = 2.1353234595205777465445279430075e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.45 y1(analytic)= = -0.25938850278962629877205672974446 y1(numeric) = = -0.25938850278542493855324967190877 absolute error = 4.20136021880705783569e-12 relative error = 1.6197172093685728540037188231799e-09 % glob_h = 0.01 y2(analytic)= = -0.96577306062063878103760801869169 y2(numeric) = = -0.96577306059998238761191227944359 absolute error = 2.065639342569573924810e-11 relative error = 2.1388454770545406134056676860516e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.46 y1(analytic)= = -0.24971796382773057335341360111266 y1(numeric) = = -0.24971796382372680072767097997506 absolute error = 4.00377262574262113760e-12 relative error = 1.6033178247859843842397081265575e-09 % glob_h = 0.01 y2(analytic)= = -0.96831861416670713762908092824644 y2(numeric) = = -0.96831861414596218394348164171803 absolute error = 2.074495368559928652841e-11 relative error = 2.1423685739483063579025465784651e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.47 y1(analytic)= = -0.24002245327754968440743865533016 y1(numeric) = = -0.24002245327374485133620666556238 absolute error = 3.80483307123198976778e-12 relative error = 1.5851988092265166024035791406561e-09 % glob_h = 0.01 y2(analytic)= = -0.97076733665828831220992179927159 y2(numeric) = = -0.97076733663745668908626633936172 absolute error = 2.083162312365545990987e-11 relative error = 2.1458924643432070137663969145774e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.48 y1(analytic)= = -0.23030294068205908482980140684885 y1(numeric) = = -0.23030294067845452516968932351475 absolute error = 3.60455966011208333410e-12 relative error = 1.5651383562176474974056850224408e-09 % glob_h = 0.01 y2(analytic)= = -0.97311898322517374193699541853268 y2(numeric) = = -0.97311898320425735838890207937582 absolute error = 2.091638354809333915686e-11 relative error = 2.1494168656304402573446721963332e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.49 y1(analytic)= = -0.2205603979844187568494820065161 y1(numeric) = = -0.22056039798101578612354078288169 absolute error = 3.40297072594122363441e-12 relative error = 1.5428747667483002562069370232856e-09 % glob_h = 0.01 y2(analytic)= = -0.97537331870466643720739369365918 y2(numeric) = = -0.97537331868366722026676490696981 absolute error = 2.099921694062878668937e-11 relative error = 2.1529414981862083845666322456926e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.5 y1(analytic)= = -0.21079579943077970598048182479383 y1(numeric) = = -0.21079579942757962115114667051334 absolute error = 3.20008482933515428049e-12 relative error = 1.5180970578998589236451732123310e-09 % glob_h = 0.01 y2(analytic)= = -0.97753011766509705538913501449863 y2(numeric) = = -0.97753011764401694992991453023626 absolute error = 2.108010545922048426237e-11 relative error = 2.1564660851137634902979670562311e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.51 y1(analytic)= = -0.20101012147286015779035832174077 y1(numeric) = = -0.20101012146986423703408751751332 absolute error = 2.99592075627080422745e-12 relative error = 1.4904327873237494332694236659802e-09 % glob_h = 0.01 y2(analytic)= = -0.97958916442836687989632919704766 y2(numeric) = = -0.97958916440720784845551920567473 absolute error = 2.115903144080999137293e-11 relative error = 2.1599903519918180818138276557397e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.52 y1(analytic)= = -0.19120434267030119978472111819888 y1(numeric) = = -0.19120434266751070226836316934918 absolute error = 2.79049751635794884970e-12 relative error = 1.4594320805619352010584731740889e-09 % glob_h = 0.01 y2(analytic)= = -0.98155025309151545032968624674211 y2(numeric) = = -0.98155025307027947292564079093668 absolute error = 2.123597740404545580543e-11 relative error = 2.1635140266288033039725295282078e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.53 y1(analytic)= = -0.1813794435928116327621307913814 y1(numeric) = = -0.1813794435902277984210518650093 absolute error = 2.58383434107892637210e-12 relative error = 1.4245464038799863200621004185007e-09 % glob_h = 0.01 y2(analytic)= = -0.98341318754731068693732785543696 y2(numeric) = = -0.98341318752599976088533924723217 absolute error = 2.131092605198860820479e-11 relative error = 2.1670368388224779820901203256043e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.54 y1(analytic)= = -0.1715364067221118170727192195978 y1(numeric) = = -0.17153640671973586639072264798104 absolute error = 2.37595068199657161676e-12 relative error = 1.3850999489837750284216373482383e-09 % glob_h = 0.01 y2(analytic)= = -0.98517778150385945040061393078254 y2(numeric) = = -0.9851777814824755901258092566884 absolute error = 2.138386027480467409414e-11 relative error = 2.1705585201244109121881874896550e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.55 y1(analytic)= = -0.16167621635368631931419242500794 y1(numeric) = = -0.1616762163515194531052618918435 absolute error = 2.16686620893053316444e-12 relative error = 1.3402504448707846405710238322424e-09 % glob_h = 0.01 y2(analytic)= = -0.98684385850323657590534765402509 y2(numeric) = = -0.98684385848178181275291281569978 absolute error = 2.145476315243483832531e-11 relative error = 2.1740788036088763493671906521943e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.56 y1(analytic)= = -0.1517998584983551841186737926099 y1(numeric) = = -0.15179985849639858331057164845832 absolute error = 1.95660080810214415158e-12 relative error = 1.2889345401618702771033751425717e-09 % glob_h = 0.01 y2(analytic)= = -0.98841125193913051861047608903809 y2(numeric) = = -0.98841125191760690065322519046878 absolute error = 2.152361795725089856931e-11 relative error = 2.1775974236457185564126684803867e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.57 y1(analytic)= = -0.14190832078367367382118531437459 y1(numeric) = = -0.14190832078192849924093729334386 absolute error = 1.74517458024802103073e-12 relative error = 1.2297901705907583294408545761122e-09 % glob_h = 0.01 y2(analytic)= = -0.98987980507350384596444412806507 y2(numeric) = = -0.98987980505191343780775238194682 absolute error = 2.159040815669174611825e-11 relative error = 2.1811141156767556600828127616505e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=122.0MB, alloc=4.4MB, time=6.67 x[1] = = 4.58 y1(analytic)= = -0.1320025923551703359536334006823 y1(numeric) = = -0.13200259235363772811493083196959 absolute error = 1.53260783870256871271e-12 relative error = 1.1610437426705119179012060220283e-09 % glob_h = 0.01 y2(analytic)= = -0.99124937105226691083385383609731 y2(numeric) = = -0.9912493710306117934179725221168 absolute error = 2.165511741588131398051e-11 relative error = 2.1846286159953059974992789469428e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.59 y1(analytic)= = -0.1220836637774332746752485243965 y1(numeric) = = -0.12208366377611435356779894981437 absolute error = 1.31892110744957458213e-12 relative error = 1.0803420102578641616363340302267e-09 % glob_h = 0.01 y2(analytic)= = -0.99251981291996313809017767868781 y2(numeric) = = -0.99251981289824540848995004468124 absolute error = 2.171772960022763400657e-11 relative error = 2.1881406615284316874619593619606e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.6 y1(analytic)= = -0.11215252693505451742990782122919 y1(numeric) = = -0.11215252693395038231076474329477 absolute error = 1.10413511914307793442e-12 relative error = 9.8449419671342977528280708485928e-10 % glob_h = 0.01 y2(analytic)= = -0.99369100363346445613810465990883 y2(numeric) = = -0.99369100361168622736010201332411 absolute error = 2.177822877800264658472e-11 relative error = 2.1916499896215043920965549870266e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.61 y1(analytic)= = -0.10221017493344238231112882817269 y1(numeric) = = -0.10221017493255411149803112275217 absolute error = 8.8827081309770542052e-13 relative error = 8.6906300050472768476462269516034e-10 % glob_h = 0.01 y2(analytic)= = -0.99476282607467550385377935740314 y2(numeric) = = -0.9947628260528389046308769491112 absolute error = 2.183659922290240829194e-11 relative error = 2.1951563378247071967173840659281e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.62 y1(analytic)= = -0.09225760199951176481534177561582 y1(numeric) = = -0.092257601998840415482093108509796 absolute error = 6.71349333248667106024e-13 relative error = 7.2768998835697024141424580402555e-10 % glob_h = 0.01 y2(analytic)= = -0.99573517306224534252282683445147 y2(numeric) = = -0.99573517304035251710623948967388 absolute error = 2.189282541658734477759e-11 relative error = 2.1986594436810942778617928672523e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.63 y1(analytic)= = -0.082295803382262274872007287402623 y1(numeric) = = -0.082295803381808882845925675650367 absolute error = 4.53392026081611752256e-13 relative error = 5.5092970412551334157368112428148e-10 % glob_h = 0.01 y2(analytic)= = -0.9966079473622855016167293539807 y2(numeric) = = -0.99660794734033860956552715588692 absolute error = 2.194689205120219809378e-11 relative error = 2.2021590445158365923563749314725e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.64 y1(analytic)= = -0.072325775253254166254025200760118 y1(numeric) = = -0.072325775253019745815492656851092 absolute error = 2.34420438532543909026e-13 relative error = 3.2411742247034758087927119151396e-10 % glob_h = 0.01 y2(analytic)= = -0.99738106169809328661190893188283 y2(numeric) = = -0.99738106167609450258003361221474 absolute error = 2.199878403187531966809e-11 relative error = 2.2056548772262872399123233954049e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.65 y1(analytic)= = -0.062348514606992010692557016177074 y1(numeric) = = -0.062348514606977554376699006806177 absolute error = 1.4456315858009370897e-14 relative error = 2.3186303553714785810335142693675e-11 % glob_h = 0.01 y2(analytic)= = -0.99805443875887937652883655089603 y2(numeric) = = -0.99805443873683089004963958875594 absolute error = 2.204848647919696214009e-11 relative error = 2.2091466780725044582113139447210e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.66 y1(analytic)= = -0.052365019161226078245837166795957 y1(numeric) = = -0.052365019161432556646361407305476 absolute error = 2.06478400524240509519e-13 relative error = 3.9430597721833433529539139740445e-10 % glob_h = 0.01 y2(analytic)= = -0.99862801120749883843868709783252 y2(numeric) = = -0.99862801118540285370701087247875 absolute error = 2.209598473167622535377e-11 relative error = 2.2126341824678734278215456779572e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.67 y1(analytic)= = -0.042376287257181393700854320105276 y1(numeric) = = -0.042376287257609755276078211341877 absolute error = 4.28361575223891236601e-13 relative error = 1.0108520659777667757099624175646e-09 % glob_h = 0.01 y2(analytic)= = -0.99910172168718478584253184927338 y2(numeric) = = -0.99910172166504352149435553536103 absolute error = 2.214126434817631391235e-11 relative error = 2.2161171247694702143830299505878e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.68 y1(analytic)= = -0.032383317759724446019120367944567 y1(numeric) = = -0.032383317760375616900216163945348 absolute error = 6.51170881095796000781e-13 relative error = 2.0108220100463754979937133609763e-09 % glob_h = 0.01 y2(analytic)= = -0.99947552282728400756284194975967 y2(numeric) = = -0.99947552280509969645251418389938 absolute error = 2.218431111032776586029e-11 relative error = 2.2195952380678122723578417102332e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.69 y1(analytic)= = -0.022387109957477534072388396442007 y1(numeric) = = -0.0223871099583524178738749691714 absolute error = 8.74883801486572729393e-13 relative error = 3.9079800972449871140216064360062e-09 % glob_h = 0.01 y2(analytic)= = -0.99974937724799399358919340694292 y2(numeric) = = -0.99974937722576888256427409268279 absolute error = 2.222511102491931426013e-11 relative error = 2.2230682539756399885090658637066e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.7 y1(analytic)= = -0.012388663462890737150508296327111 y1(numeric) = = -0.012388663463990214783018137638457 absolute error = 1.099477632509841311346e-12 relative error = 8.8748688331331278324008854178453e-09 % glob_h = 0.01 y2(analytic)= = -0.99992325756410088417953654157497 y2(numeric) = = -0.99992325754183723385327049589823 absolute error = 2.226365032626604567674e-11 relative error = 2.2265359024153727594156817732783e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.71 y1(analytic)= = -0.0023889781122815029610961477246958 y1(numeric) = = -0.0023889781136064324464460188394751 absolute error = 1.3249294853498711147793e-12 relative error = 5.5460093105857192150768082132545e-08 % glob_h = 0.01 y2(analytic)= = -0.99999714638771796842523471259357 y2(numeric) = = -0.99999714636541805294668019072219 absolute error = 2.229991547855452187138e-11 relative error = 2.2299979114048810768661763387225e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.72 y1(analytic)= = 0.0076109461341481509210826531746326 y1(numeric) = = 0.0076109461325969346324892480675512 absolute error = 1.5512162885934051070814e-12 relative error = 2.0381385720673264935852116073648e-08 % glob_h = 0.01 y2(analytic)= = -0.99997103633002445843229788796164 y2(numeric) = = -0.99997103630769056525413335462228 absolute error = 2.233389317816453333936e-11 relative error = 2.2334540068412130337890935937511e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=6.87 NO POLE NO POLE x[1] = = 4.73 y1(analytic)= = 0.017610109292306823958480184942845 y1(numeric) = = 0.017610109290528509167890761842133 absolute error = 1.778314790589423100712e-12 relative error = 1.0098260953816454126273695557966e-08 % glob_h = 0.01 y2(analytic)= = -0.99984493000200436524284191155768 y2(numeric) = = -0.99984492997963879488687475585707 absolute error = 2.236557035596715570061e-11 relative error = 2.2369039122819095533220787030732e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.74 y1(analytic)= = 0.027607511454211308473521317218995 y1(numeric) = = 0.027607511452205106911684714332623 absolute error = 2.006201561836602886372e-12 relative error = 7.2668685301969607122997730134231e-09 % glob_h = 0.01 y2(analytic)= = -0.99961884001418540260979704807277 y2(numeric) = = -0.99961883999179046843019826570322 absolute error = 2.239493417959878236955e-11 relative error = 2.2403473487235374713701526815934e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.75 y1(analytic)= = 0.037602152887976554715496312373334 y1(numeric) = = 0.03760215288574170171809807809541 absolute error = 2.234852997398234277924e-12 relative error = 5.9434176656221134853680177245926e-09 % glob_h = 0.01 y2(analytic)= = -0.99929278897537794473427075559708 y2(numeric) = = -0.99929278895295597267855994620642 absolute error = 2.242197205571080939066e-11 relative error = 2.2437840343770633509142564028079e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.76 y1(analytic)= = 0.047593034137788026258408716410526 y1(numeric) = = 0.047593034135323780939064379029147 absolute error = 2.464245319344337381379e-12 relative error = 5.1777436845275015535869118744955e-09 % glob_h = 0.01 y2(analytic)= = -0.99886680949041416406874008456944 y2(numeric) = = -0.99886680946796749243654543374137 absolute error = 2.244667163219465082807e-11 relative error = 2.2472136844396835517123275680376e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.77 y1(analytic)= = 0.057579156123846448577548772787261 y1(numeric) = = 0.057579156121152093998328040073454 absolute error = 2.694354579220732713807e-12 relative error = 4.6793922672737189405417127703201e-09 % glob_h = 0.01 y2(analytic)= = -0.99834094415688757527040933829949 y2(numeric) = = -0.99834094413441855447002757265842 absolute error = 2.246902080038176564107e-11 relative error = 2.2506360108627175943476896849205e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.78 y1(analytic)= = 0.067559520242274956413221714659554 y1(numeric) = = 0.067559520239349799752676907521969 absolute error = 2.925156660544807137585e-12 relative error = 4.3297475323313623170008448531846e-09 % glob_h = 0.01 y2(analytic)= = -0.99771524556089331134762062164767 y2(numeric) = = -0.99771524553840430365040224208461 absolute error = 2.248900769721837956306e-11 relative error = 2.2540507221151622102690545049585e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.79 y1(analytic)= = 0.077533128464978649290150241347593 y1(numeric) = = 0.077533128461822022008822525406062 absolute error = 3.156627281327715941531e-12 relative error = 4.0713271137428043917769567581848e-09 % glob_h = 0.01 y2(analytic)= = -0.99698977627176955796815287876274 y2(numeric) = = -0.99698977624926293726073829063509 absolute error = 2.250662070741458812765e-11 relative error = 2.2574575229424926215321965791644e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.8 y1(analytic)= = 0.087498983439446569320215257649488 y1(numeric) = = 0.087498983436057827323592499856003 absolute error = 3.388741996622757793485e-12 relative error = 3.8728929907716326395427698529443e-09 % glob_h = 0.01 y2(analytic)= = -0.99616460883584067178159646650363 y2(numeric) = = -0.99616460881331882331602893685012 absolute error = 2.252184846556752965351e-11 relative error = 2.2608561141202855021759323947796e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.81 y1(analytic)= = 0.097456088588486121173922639538394 y1(numeric) = = 0.09745608858486464497282298382893 absolute error = 3.621476201099655709464e-12 relative error = 3.7160081566494475397894928161452e-09 % glob_h = 0.01 y2(analytic)= = -0.99523982576916260843875697540403 y2(numeric) = = -0.99523982574662792858049865569598 absolute error = 2.253467985825831970805e-11 relative error = 2.2642461922022246883691715054020e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.82 y1(analytic)= = 0.10740344820987996086171061916977 y1(numeric) = = 0.1074034482060251557300661455369 absolute error = 3.85480513164447363287e-12 relative error = 3.5890888010519880720496501425908e-09 % glob_h = 0.01 y2(analytic)= = -0.99421551954927138575924090129834 y2(numeric) = = -0.99421551952672628173311845998005 absolute error = 2.254510402612244131829e-11 relative error = 2.2676274492620359714855233170382e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.83 y1(analytic)= = 0.11734006757595538771926678895382 y1(numeric) = = 0.11734006757186668384928189425987 absolute error = 4.08870386998489469395e-12 relative error = 3.4844908090224476732253318326091e-09 % glob_h = 0.01 y2(analytic)= = -0.9930917926059354071940301512694 y2(numeric) = = -0.99309179258338229682813686328228 absolute error = 2.255311036589328798712e-11 relative error = 2.2709995726288811658345177826377e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.84 y1(analytic)= = 0.12726495303305628274063040973268 y1(numeric) = = 0.12726495302873313539528982600736 absolute error = 4.32314734534058372532e-12 relative error = 3.3969661264226239866417086270183e-09 % glob_h = 0.01 y2(analytic)= = -0.99186875731091257034299275504052 y2(numeric) = = -0.99186875728835388181057419563933 absolute error = 2.255868853241855940119e-11 relative error = 2.2743622446157240224015512664681e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.85 y1(analytic)= = 0.13717711210090764614813971846528 y1(numeric) = = 0.13717711209634953581104136532141 absolute error = 4.55811033709835314387e-12 relative error = 3.3227921679422743502609308114854e-09 % glob_h = 0.01 y2(analytic)= = -0.99054653596671318480794231629118 y2(numeric) = = -0.99054653594415135636729310370538 absolute error = 2.256182844064921258580e-11 relative error = 2.2777151422401613866023348871851e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.86 y1(analytic)= = 0.1470755535718627978282707459854 y1(numeric) = = 0.14707555356706923035075889811119 absolute error = 4.79356747751184787421e-12 relative error = 3.2592550978702629682912497671025e-09 % glob_h = 0.01 y2(analytic)= = -0.98912526079436982308009669404291 y2(numeric) = = -0.98912526077180730281249601987334 absolute error = 2.256252026760067416957e-11 relative error = 2.2810579369371921885371244885666e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=7.07 NO POLE NO POLE x[1] = = 4.87 y1(analytic)= = 0.15695928761002331599602978562804 y1(numeric) = = 0.15695928760499382274160432404519 absolute error = 5.02949325442546158285e-12 relative error = 3.2043298176286329421860074603633e-09 % glob_h = 0.01 y2(analytic)= = -0.98760507392021532746665541129251 y2(numeric) = = -0.98760507389765457301236938892399 absolute error = 2.256075445428602236852e-11 relative error = 2.2843902942633743175950450852826e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.88 y1(analytic)= = 0.16682732585022180217663274703162 y1(numeric) = = 0.16682732584495594016261055391387 absolute error = 5.26586201402219311775e-12 relative error = 3.1564745087084257117730613695611e-09 % glob_h = 0.01 y2(analytic)= = -0.98598612736167029524478484231842 y2(numeric) = = -0.98598612733911377353716399203378 absolute error = 2.255652170762085028464e-11 relative error = 2.2877118735917950696552301261041e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.89 y1(analytic)= = 0.17667868149685757431045858971384 y1(numeric) = = 0.17667868149135492634686344100987 absolute error = 5.50264796359514870397e-12 relative error = 3.1144945824677887817658653281606e-09 % glob_h = 0.01 y2(analytic)= = -0.9842685830120414632826520572489 y2(numeric) = = -0.98426858298949165028035253211122 absolute error = 2.254981300229952513768e-11 relative error = 2.2910223277972545553941482592405e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.9 y1(analytic)= = 0.18651236942257540449432914412192 y1(numeric) = = 0.18651236941683557931998675198876 absolute error = 5.73982517434239213316e-12 relative error = 3.0774501402305628078582819052813e-09 % glob_h = 0.01 y2(analytic)= = -0.98245261262433251227637724991833 y2(numeric) = = -0.98245261260179189269373468880757 absolute error = 2.254061958264256111076e-11 relative error = 2.2943213029310331031496681774024e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.91 y1(analytic)= = 0.1963274062667774335675731995194 y1(numeric) = = 0.19632740626080006598338835761475 absolute error = 5.97736758418484190465e-12 relative error = 3.0445915309768615573183111015893e-09 % glob_h = 0.01 y2(analytic)= = -0.98053839779406890950899010226969 y2(numeric) = = -0.98053839777153997654457527567977 absolute error = 2.252893296441482658992e-11 relative error = 2.2976084378845831493147889821282e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.92 y1(analytic)= = 0.20612281053395841143350924081177 y1(numeric) = = 0.20612281052774316243290232978495 absolute error = 6.21524900060691102682e-12 relative error = 3.0153135329886055727332739485856e-09 % glob_h = 0.01 y2(analytic)= = -0.97852612994113850763280160634113 y2(numeric) = = -0.9785261299186237626961872966267 absolute error = 2.251474493661430971443e-11 relative error = 2.3008833640414532415331001563722e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.93 y1(analytic)= = 0.21589760269185442967426044648577 y1(numeric) = = 0.21589760268540098657074086451355 absolute error = 6.45344310351958197222e-12 relative error = 2.9891221685913898388019863266675e-09 % glob_h = 0.01 y2(analytic)= = -0.97641601029064971540018032274914 y2(numeric) = = -0.97641601026815166783694915342045 absolute error = 2.249804756323116932869e-11 relative error = 2.3041457049167164306271550164850e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.94 y1(analytic)= = 0.22565080526939533166743080403972 y1(numeric) = = 0.22565080526270340821928519794303 absolute error = 6.69192344814560609669e-12 relative error = 2.9656102667820708561305866913280e-09 % glob_h = 0.01 y2(analytic)= = -0.97420824985280915450970852682316 y2(numeric) = = -0.97420824983033032132473172518594 absolute error = 2.247883318497680163722e-11 relative error = 2.3073950757831373279857311318848e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.95 y1(analytic)= = 0.23538144295445100504525741163474 y1(numeric) = = 0.23538144294752034157733089795042 absolute error = 6.93066346792651368432e-12 relative error = 2.9444391966225120581978296473919e-09 % glob_h = 0.01 y2(analytic)= = -0.97190306940182081478526506337735 y2(numeric) = = -0.97190306937936372036428240726646 absolute error = 2.245709442098265611089e-11 relative error = 2.3106310832832712729462080548959e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.96 y1(analytic)= = 0.24508854269136178194844802293532 y1(numeric) = = 0.24508854268419214547099690527129 absolute error = 7.16963647745111766403e-12 relative error = 2.9253250269147785905748584533134e-09 % glob_h = 0.01 y2(analytic)= = -0.96950069945380881775493302309673 y2(numeric) = = -0.9695006994313759935844644856209 absolute error = 2.243282417046853747583e-11 relative error = 2.3138533250266451903758115464876e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.97 y1(analytic)= = 0.25477113377824319411595351401254 y1(numeric) = = 0.25477113377083437844054832304913 absolute error = 7.40881567540519096341e-12 relative error = 2.9080279094153346153987989737834e-09 % glob_h = 0.01 y2(analytic)= = -0.96700138024376599633497671407791 y2(numeric) = = -0.96700138022135998072059658014321 absolute error = 2.240601561438013393470e-11 relative error = 2.3170613891711226051915211054260e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.98 y1(analytic)= = 0.26442824796405535241625332068078 y1(numeric) = = 0.26442824795640717826871132626208 absolute error = 7.64817414754199441870e-12 relative error = 2.8923438423952486421795486856154e-09 % glob_h = 0.01 y2(analytic)= = -0.96440536170153059574171007792892 y2(numeric) = = -0.96440536167915393352471456280481 absolute error = 2.237666221699551512411e-11 relative error = 2.3202548539875046820903677133767e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 4.99 y1(analytic)= = 0.27405891954542724396309159769695 y1(numeric) = = 0.27405891953753955909341826854789 absolute error = 7.88768486967332914906e-12 relative error = 2.8780982143388653518116569519009e-09 % glob_h = 0.01 y2(analytic)= = -0.96171290342679349794114601441111 y2(numeric) = = -0.96171290340444874021364566771038 absolute error = 2.234475772750034670073e-11 relative error = 2.3234332874063648183245197875201e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5 y1(analytic)= = 0.28366218546322626446663917151356 y1(numeric) = = 0.28366218545509894375595838718596 absolute error = 8.12732071068078432760e-12 relative error = 2.8651406945232055223175530592158e-09 % glob_h = 0.01 y2(analytic)= = -0.95892427466313846889315440615599 y2(numeric) = = -0.95892427464082817271162283428424 absolute error = 2.231029618153157187175e-11 relative error = 2.3265962465460559553088218866025e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=133.5MB, alloc=4.4MB, time=7.28 x[1] = = 5.01 y1(analytic)= = 0.29323708539886332894732051243469 y1(numeric) = = 0.29323708539049627451177366409265 absolute error = 8.36705443554684834204e-12 relative error = 2.8533411536831764748430102890113e-09 % glob_h = 0.01 y2(analytic)= = -0.9560397542711180245437713724687 y2(numeric) = = -0.95603975424884475264108205882537 absolute error = 2.227327190268931364333e-11 relative error = 2.3297432772207670867615131790000e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.02 y1(analytic)= = 0.30278266187032393038148833489222 y1(numeric) = = 0.30278266186171707167308278645779 absolute error = 8.60685870840554843443e-12 relative error = 2.8425863803561191783124398003537e-09 % glob_h = 0.01 y2(analytic)= = -0.9530596307003676079566238177417 y2(numeric) = = -0.95305963067813392845260706269031 absolute error = 2.223367950401675505139e-11 relative error = 2.3328739134274380950617090599546e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.03 y1(analytic)= = 0.31229796032791554325310687383438 y1(numeric) = = 0.3122979603190688371574945927917 absolute error = 8.84670609561228104268e-12 relative error = 2.8327774175416206960804556261660e-09 % glob_h = 0.01 y2(analytic)= = -0.9499842019607608661425180237609 y2(numeric) = = -0.94998420193856935225307026559628 absolute error = 2.219151388944775816462e-11 relative error = 2.3359876768102696823602404678867e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.04 y1(analytic)= = 0.32178202924972179735087790589445 y1(numeric) = = 0.32178202924063522828204541365718 absolute error = 9.08656906883249223727e-12 relative error = 2.8238273871350285170928776661421e-09 % glob_h = 0.01 y2(analytic)= = -0.94681377559260891103547213786007 y2(numeric) = = -0.94681377557046214078025015165345 absolute error = 2.214677025522198620662e-11 relative error = 2.3390840761014873843624466942921e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.05 y1(analytic)= = 0.33123392023675387647297468241818 y1(numeric) = = 0.33123392022742745646482581756437 absolute error = 9.32642000814886485381e-12 relative error = 2.8156597010000308432798967836862e-09 % glob_h = 0.01 y2(analytic)= = -0.94354866863590654466426108726801 y2(numeric) = = -0.94354866861380710057299379053282 absolute error = 2.209944409126729673519e-11 relative error = 2.3421626065369350331744184658473e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.06 y1(analytic)= = 0.34065268810778962697880586890168 y1(numeric) = = 0.34065268809822339577361920273363 absolute error = 9.56623120518666616805e-12 relative error = 2.8082065808210240131111895594195e-09 % glob_h = 0.01 y2(analytic)= = -0.94018920759862852387132870489351 y2(numeric) = = -0.94018920757657899268877952745443 absolute error = 2.204953118254917743908e-11 relative error = 2.3452227492449831019789791095910e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.07 y1(analytic)= = 0.35003739099389089235598664146424 y1(numeric) = = 0.35003739098408491748972973422049 absolute error = 9.80597486625690724375e-12 relative error = 2.8014078262936339459249634449316e-09 % glob_h = 0.01 y2(analytic)= = -0.93673572842407903492617548400048 y2(numeric) = = -0.93673572840208200731578848423313 absolute error = 2.199702761038699976735e-11 relative error = 2.3482639706071406068201285671679e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.08 y1(analytic)= = 0.35938709043258962214782442617103 y1(numeric) = = 0.35938709042254399903230746376547 absolute error = 1.004562311551696240556e-11 relative error = 2.7952097843651464945877145601703e-09 % glob_h = 0.01 y2(analytic)= = -0.93318857645729764305855194253795 y2(numeric) = = -0.93318857643535571330481507324561 absolute error = 2.194192975373686929234e-11 relative error = 2.3512857215886551000751657945017e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.09 y1(analytic)= = 0.36870085146173333670891469511059 y1(numeric) = = 0.36870085145144818871076640045965 absolute error = 1.028514799814829465094e-11 relative error = 2.7895644822550044744478247132908e-09 % glob_h = 0.01 y2(analytic)= = -0.92954810641052507628850932904951 y2(numeric) = = -0.92954810638864084199806847362488 absolute error = 2.188423429044085542463e-11 relative error = 2.3542874370372731551434029109868e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.1 y1(analytic)= = 0.37797774271298056332057555292898 y1(numeric) = = 0.37797774270245604183702462271415 absolute error = 1.052452148355093021483e-11 relative error = 2.7844288946777435895407164992717e-09 % glob_h = 0.01 y2(analytic)= = -0.92581468232773229694614624754486 y2(numeric) = = -0.92581468230590835874770386069904 absolute error = 2.182393819844238684582e-11 relative error = 2.3572685349482129438778387746601e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.11 y1(analytic)= = 0.38721683650493689420042217408235 y1(numeric) = = 0.38721683649417317873186785114132 absolute error = 1.076371546855432294103e-11 relative error = 2.7797643216418067393227775760197e-09 % glob_h = 0.01 y2(analytic)= = -0.92198867754821640794434021813427 y2(numeric) = = -0.92198867752645536918737261533108 absolute error = 2.176103875696760280319e-11 relative error = 2.3602284156932703158777234272122e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.12 y1(analytic)= = 0.39641720893592235287789325632821 y1(numeric) = = 0.39641720892491965109724900973389 absolute error = 1.100270178064424659432e-11 relative error = 2.7755358578347552684199673025943e-09 % glob_h = 0.01 y2(analytic)= = -0.91807047466926703418350025661942 y2(numeric) = = -0.91807047464757150063582780240151 absolute error = 2.169553354767245421791e-11 relative error = 2.3631664612118394007014264860689e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.13 y1(analytic)= = 0.40557793997636079227639781876946 y1(numeric) = = 0.40557793996511934009519246800253 absolute error = 1.124145218120535076693e-11 relative error = 2.7717119382431306568377890231912e-09 % glob_h = 0.01 y2(analytic)= = -0.91406046550790691241908875265767 y2(numeric) = = -0.91406046548627949196333340026178 absolute error = 2.162742045575535239589e-11 relative error = 2.3660820341614772925199944957860e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.14 y1(analytic)= = 0.41469811356078208563926503820328 y1(numeric) = = 0.4146981135493021472704860246089 absolute error = 1.147993836877901359438e-11 relative error = 2.7682639475273149587339630957440e-09 % glob_h = 0.01 y2(analytic)= = -0.90995905106171051550104315881085 y2(numeric) = = -0.90995905104015381783000799181446 absolute error = 2.155669767103516699639e-11 relative error = 2.3689744770254788788874232266427e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=137.3MB, alloc=4.4MB, time=7.48 x[1] = = 5.15 y1(analytic)= = 0.42377681767942791015707276566807 y1(numeric) = = 0.42377681766770977817473664357142 absolute error = 1.171813198233612209665e-11 relative error = 2.7651658829531520422281689544859e-09 % glob_h = 0.01 y2(analytic)= = -0.90576664146870462909002251067931 y2(numeric) = = -0.90576664144722126540102813187116 absolute error = 2.148336368899437880815e-11 relative error = 2.3718431111747512846767704852391e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.16 y1(analytic)= = 0.43281314446945196279432988889981 y1(numeric) = = 0.43281314445749595818976548029554 absolute error = 1.195600460456440860427e-11 relative error = 2.7623940625047873910518871767695e-09 % glob_h = 0.01 y2(analytic)= = -0.90148365596635489075939107878676 y2(numeric) = = -0.90148365594494747344760388198084 absolute error = 2.140741731178719680592e-11 relative error = 2.3746872358810865585515382902794e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.17 y1(analytic)= = 0.44180619030570548836992979898352 y1(numeric) = = 0.4418061902935119606047598295706 absolute error = 1.219352776516996941292e-11 relative error = 2.7599268712674038117164133588735e-09 % glob_h = 0.01 y2(analytic)= = -0.89711052284964239279485118369484 y2(numeric) = = -0.8971105228283135351456387307845 absolute error = 2.132885764921245291034e-11 relative error = 2.3775061272787248572350199255379e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.18 y1(analytic)= = 0.45075505589109904141422127040521 y1(numeric) = = 0.45075505587866836847002868086857 absolute error = 1.243067294419258953664e-11 relative error = 2.7577445403509350267674303668919e-09 % glob_h = 0.01 y2(analytic)= = -0.89264767942823454099650916318622 y2(numeric) = = -0.89264767940698685687685807133379 absolute error = 2.124768411965109185243e-11 relative error = 2.3802990372708770798057195156490e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.19 y1(analytic)= = 0.45965884634653144570181226462633 y1(numeric) = = 0.45965884633386403412647776942772 absolute error = 1.266741157533449519861e-11 relative error = 2.7558289535854339426073551211013e-09 % glob_h = 0.01 y2(analytic)= = -0.8880955719827544523618034528906 y2(numeric) = = -0.88809557196159055591083537534283 absolute error = 2.116389645096807754777e-11 relative error = 2.3830651923776341259328748329573e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.2 y1(analytic)= = 0.46851667130037695863909392660865 y1(numeric) = = 0.46851667128747324358979177309938 absolute error = 1.290371504930215350927e-11 relative error = 2.7541634780012515324350432619213e-09 % glob_h = 0.01 y2(analytic)= = -0.8834546557201532646730844404218 y2(numeric) = = -0.88345465569907576999170589900484 absolute error = 2.107749468137854141696e-11 relative error = 2.3858037925214279975040342359292e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.21 y1(analytic)= = 0.47732764497752169186461841030444 y1(numeric) = = 0.47732764496438213714745767366887 absolute error = 1.313955471716073663557e-11 relative error = 2.7527328147481389643402802587204e-09 % glob_h = 0.01 y2(analytic)= = -0.87872539472818982072169771699585 y2(numeric) = = -0.87872539470720134156141971485045 absolute error = 2.098847916027800214540e-11 relative error = 2.3885140097459259564676366052308e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.22 y1(analytic)= = 0.48609088628794038449446726517369 y1(numeric) = = 0.48609088627456548260076639951122 absolute error = 1.337490189370086566247e-11 relative error = 2.7515228676346999309815188403393e-09 % glob_h = 0.01 y2(analytic)= = -0.87390826192902227916221484816978 y2(numeric) = = -0.87390826190812542861317835771229 absolute error = 2.089685054903649045749e-11 relative error = 2.3911949868639308229761757478133e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.23 y1(analytic)= = 0.49480551891480467140909957854779 y1(numeric) = = 0.49480551890119494354828233125986 absolute error = 1.360972786081724728793e-11 relative error = 2.7505206269052472662461187370472e-09 % glob_h = 0.01 y2(analytic)= = -0.86900373903191629279705271191494 y2(numeric) = = -0.8690037390111136829752962953269 absolute error = 2.080260982175641658804e-11 relative error = 2.3938458360295259606360292234659e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.24 y1(analytic)= = 0.50347067140211403582827450118648 y1(numeric) = = 0.50347067138827003195737568670943 absolute error = 1.384400387089881447705e-11 relative error = 2.7497140662324356668603244209766e-09 % glob_h = 0.01 y2(analytic)= = -0.86401231648507448343424322202706 y2(numeric) = = -0.86401231646436872516824919976231 absolute error = 2.070575826599402226475e-11 relative error = 2.3964656372293400218476322931066e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.25 y1(analytic)= = 0.5120854772418406831518162141691 y1(numeric) = = 0.51208547722776298200158623393994 absolute error = 1.407770115022998022916e-11 relative error = 2.7490920512048728208813971821615e-09 % glob_h = 0.01 y2(analytic)= = -0.85893449342659203033072568942271 y2(numeric) = = -0.85893449340598573284728142625076 absolute error = 2.060629748344426317195e-11 relative error = 2.3990534366874113189987028826574e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.26 y1(analytic)= = 0.5206490749605796216514577467554 y1(numeric) = = 0.5206490749462688307490551350713 absolute error = 1.431079090240261168410e-11 relative error = 2.7486442578403001388211680931178e-09 % glob_h = 0.01 y2(analytic)= = -0.85377077763454327662144728535596 y2(numeric) = = -0.85377077761403904723085831331123 absolute error = 2.050422939058897204473e-11 relative error = 2.4016082451777016483861886378763e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.27 y1(analytic)= = 0.52916060820569528507790262071643 y1(numeric) = = 0.52916060819115204076616429080552 absolute error = 1.454324431173832991091e-11 relative error = 2.7483610998657482666530931875373e-09 % glob_h = 0.01 y2(analytic)= = -0.8485216854762043450320343405149 y2(numeric) = = -0.84852168545580478881272618376952 absolute error = 2.039955621930815674538e-11 relative error = 2.4041290362378410888389528098940e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.28 y1(analytic)= = 0.53761922583095608259263222784782 y1(numeric) = = 0.53761922581618105004591148896396 absolute error = 1.477503254672073888386e-11 relative error = 2.7482336636834599974775726324467e-09 % glob_h = 0.01 y2(analytic)= = -0.84318774185641684057114886700974 y2(numeric) = = -0.84318774183612456005369457511088 absolute error = 2.029228051745429189886e-11 relative error = 2.4066147442771749146198728842420e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.29 y1(analytic)= = 0.54602408198164831264082764699766 y1(numeric) = = 0.5460240819666421858773904616397 absolute error = 1.500612676343718535796e-11 relative error = 2.7482536500911211230536467556020e-09 % glob_h = 0.01 y2(analytic)= = -0.83776948016509780378923096327812 y2(numeric) = = -0.83776948014491539863984149636637 absolute error = 2.018240514938946691175e-11 relative error = 2.4090642625716270688654128725800e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=7.69 NO POLE NO POLE x[1] = = 5.3 y1(analytic)= = 0.55437433617916092944494663356083 y1(numeric) = = 0.55437433616392443133591698395305 absolute error = 1.523649810902964960778e-11 relative error = 2.7484133219517518854232292307880e-09 % glob_h = 0.01 y2(analytic)= = -0.83226744222390116356455966785459 y2(numeric) = = -0.83226744220383123026807441038694 absolute error = 2.006993329648525746765e-11 relative error = 2.4114764411372869319641583127325e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.31 y1(analytic)= = 0.56266915340503270371279349419497 y1(numeric) = = 0.56266915338956658598763912890318 absolute error = 1.546611772515436529179e-11 relative error = 2.7487054571163259169693003610067e-09 % glob_h = 0.01 y2(analytic)= = -0.82668217823203602322690501473648 y2(numeric) = = -0.82668217821208115476931982285395 absolute error = 1.995486845758519188253e-11 relative error = 2.4138500844739621494365070088677e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.32 y1(analytic)= = 0.57090770418445337291405010689662 y1(numeric) = = 0.57090770416875841616260034184912 absolute error = 1.569495675144976504750e-11 relative error = 2.7491233059939430041441391191912e-09 % glob_h = 0.01 y2(analytic)= = -0.82101424671124719814500764741474 y2(numeric) = = -0.82101424669140998369557795940041 absolute error = 1.983721444942968801433e-11 relative error = 2.4161839491692142177316820999307e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.33 y1(analytic)= = 0.57908916466921043107982449328557 y1(numeric) = = 0.57908916465328744475081214647265 absolute error = 1.592298632901234681292e-11 relative error = 2.7496605532427699806401785705871e-09 % glob_h = 0.01 y2(analytic)= = -0.81526421444996350667827784442947 y2(numeric) = = -0.81526421443024653127123450367722 absolute error = 1.971697540704334075225e-11 relative error = 2.4184767413525988519178768313410e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.34 y1(analytic)= = 0.58721271672007326351535908266569 y1(numeric) = = 0.58721271670392308591147902836012 absolute error = 1.615017760388005430557e-11 relative error = 2.7503112831221110839094069353327e-09 % glob_h = 0.01 y2(analytic)= = -0.80943265644661939961707585081744 y2(numeric) = = -0.80943265642702524383299140635529 absolute error = 1.959415578408444446215e-11 relative error = 2.4207271139889626048500726480781e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.35 y1(analytic)= = 0.59527754798860638808108061378544 y1(numeric) = = 0.59527754797222988635055785021244 absolute error = 1.637650173052276357300e-11 relative error = 2.7510699481036381715684908532050e-09 % glob_h = 0.01 y2(analytic)= = -0.80352015585215559590139766939157 y2(numeric) = = -0.80352015583268683554824103025697 absolute error = 1.946876035315663913460e-11 relative error = 2.4229336639986926441013010219077e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.36 y1(analytic)= = 0.6032828519984036217860410431167 y1(numeric) = = 0.6032828519818016919107015770586 absolute error = 1.660192987533946605810e-11 relative error = 2.7519313403894658173511429654672e-09 % glob_h = 0.01 y2(analytic)= = -0.79752730391170447450647846609238 y2(numeric) = = -0.79752730389236368030039589272138 absolute error = 1.934079420608257337100e-11 relative error = 2.4250949291917689231172223691938e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.37 y1(analytic)= = 0.61122782822573504934478502873904 y1(numeric) = = 0.6112278282089086161246232915401 absolute error = 1.682643322016173719894e-11 relative error = 2.7528905660276152088595074446638e-09 % glob_h = 0.01 y2(analytic)= = -0.79145469990546605390752968429357 y2(numeric) = = -0.79145469988625579115339020254322 absolute error = 1.921026275413948175035e-11 relative error = 2.4272093850013170130796526074835e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.38 y1(analytic)= = 0.61911168217959872906799388619274 y1(numeric) = = 0.61911168216254874610223080798623 absolute error = 1.704998296576307820651e-11 relative error = 2.7539430213524918660643546239802e-09 % glob_h = 0.01 y2(analytic)= = -0.78530295108878047147639354147072 y2(numeric) = = -0.78530295106970329974813696292635 absolute error = 1.907717172825657854437e-11 relative error = 2.4292754410010941566408286917436e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.39 y1(analytic)= = 0.62693362548116913098302648444835 y1(numeric) = = 0.62693362546389658064765276711374 absolute error = 1.727255033537371733461e-11 relative error = 2.7550843715101581616978025498142e-09 % glob_h = 0.01 y2(analytic)= = -0.7790726726314029555122358087456 y2(numeric) = = -0.77907267261246142833306163455518 absolute error = 1.894152717917417419042e-11 relative error = 2.4312914371899478202832861198757e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.4 y1(analytic)= = 0.63469287594263436240675183898074 y1(numeric) = = 0.63469287592514025582855138330559 absolute error = 1.749410657820045567515e-11 relative error = 2.7563105308561287184237217323277e-09 % glob_h = 0.01 y2(analytic)= = -0.77276448755598736235846978273423 y2(numeric) = = -0.77276448753718402688090535734304 absolute error = 1.880333547756442539119e-11 relative error = 2.4332556400247507153855125519357e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.41 y1(analytic)= = 0.64238865764541429731381358767358 y1(numeric) = = 0.64238865762769967434086244639537 absolute error = 1.771462297295114127821e-11 relative error = 2.7576176450377583071003412769564e-09 % glob_h = 0.01 y2(analytic)= = -0.76637902667578443020093620911081 y2(numeric) = = -0.76637902665712182688682257492619 absolute error = 1.866260331411363418462e-11 relative error = 2.4351662381816226658424689428201e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.42 y1(analytic)= = 0.65002020101775178775257108030822 y1(numeric) = = 0.6500202009998177169212077260969 absolute error = 1.793407083136335421132e-11 relative error = 2.7590020745945374117609838538736e-09 % glob_h = 0.01 y2(analytic)= = -0.75991692853156097967004139112055 y2(numeric) = = -0.75991692851304164197047537530165 absolute error = 1.851933769956601581890e-11 relative error = 2.4370213380233794870450593613545e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.43 y1(analytic)= = 0.65758674291166919825223461484378 y1(numeric) = = 0.65758674289351677675049773080901 absolute error = 1.815242150173688403477e-11 relative error = 2.7604603799281915907313207573229e-09 % glob_h = 0.01 y2(analytic)= = -0.75337883932774636927422611162311 y2(numeric) = = -0.7533788393093728233094972518498 absolute error = 1.837354596472885977331e-11 relative error = 2.4388189587490815072970743659125e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=7.89 NO POLE NO POLE x[1] = = 5.44 y1(analytic)= = 0.66508752667928256763188433853633 y1(numeric) = = 0.66508752666091292125941475845504 absolute error = 1.836964637246958008129e-11 relative error = 2.7619893075107633571092994759195e-09 % glob_h = 0.01 y2(analytic)= = -0.74676541286781259096601091200629 y2(numeric) = = -0.74676541284958735520557189921998 absolute error = 1.822523576043901278631e-11 relative error = 2.4405570271992661082927870162459e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.45 y1(analytic)= = 0.67252180224846576685878683486453 y1(numeric) = = 0.67252180222988004998319068097642 absolute error = 1.858571687559615388811e-11 relative error = 2.7635857772131511201114904215079e-09 % glob_h = 0.01 y2(analytic)= = -0.74007731048889446777721138257986 y2(numeric) = = -0.74007731047082005271972076529235 absolute error = 1.807441505749061728751e-11 relative error = 2.4422333722879131965531500099230e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.46 y1(analytic)= = 0.67988882619785708660327681930711 y1(numeric) = = 0.67988882617905648211294730716901 absolute error = 1.880060449032951213810e-11 relative error = 2.7652468706491545196310227661514e-09 % glob_h = 0.01 y2(analytic)= = -0.7333152009956564914490769558934 y2(numeric) = = -0.73331520097773539930255291271494 absolute error = 1.792109214652404317846e-11 relative error = 2.4438457190293798132022368731836e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.47 y1(analytic)= = 0.6871878618312007538939537370804 y1(numeric) = = 0.68718786181218647314734953955627 absolute error = 1.901428074660419752413e-11 relative error = 2.7669698204411564127738469846742e-09 % glob_h = 0.01 y2(analytic)= = -0.72647976059341291331847940416022 y2(numeric) = = -0.72647976057564763768060344869095 absolute error = 1.776527563787595546927e-11 relative error = 2.4453916821254160537551382606207e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.48 y1(analytic)= = 0.69441817925101594378347880055167 y1(numeric) = = 0.69441817923178922655485728649404 absolute error = 1.922671722862151405763e-11 relative error = 2.7687520003233534433427305684903e-09 % glob_h = 0.01 y2(analytic)= = -0.7195716728205077763953293501199 y2(numeric) = = -0.71957167280290080193393888526777 absolute error = 1.760697446139046485213e-11 relative error = 2.4468687590739003418884938740030e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.49 y1(analytic)= = 0.70157905543158591918519652504353 y1(numeric) = = 0.70157905541214803360680061254557 absolute error = 1.943788557839591249796e-11 relative error = 2.7705909160070966238080205845517e-09 % glob_h = 0.01 y2(analytic)= = -0.71259162847996165057166326425248 y2(numeric) = = -0.71259162846251545270547195137303 absolute error = 1.744619786619131287945e-11 relative error = 2.4482743227570637455514684272955e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.5 y1(analytic)= = 0.70866977429126000002742118132584 y1(numeric) = = 0.70866977427161224252811897054108 absolute error = 1.964775749930221078476e-11 relative error = 2.7724841967405644300236775898240e-09 % glob_h = 0.01 y2(analytic)= = -0.70554032557039190623191917552207 y2(numeric) = = -0.70554032555310895081150412750981 absolute error = 1.728295542041504801226e-11 relative error = 2.4496056134626601050005519225993e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.51 y1(analytic)= = 0.71568962676406113158872417627319 y1(numeric) = = 0.71568962674420482682910095266299 absolute error = 1.985630475962322361020e-11 relative error = 2.7744295875017874729962161353599e-09 % glob_h = 0.01 y2(analytic)= = -0.69841846921621343417947382130829 y2(numeric) = = -0.69841846919909617716856866789491 absolute error = 1.711725701090515341338e-11 relative error = 2.4508597302867237641170232127205e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.52 y1(analytic)= = 0.72263791087059189131706160765324 y1(numeric) = = 0.72263791085052839212096423308057 absolute error = 2.006349919609737457267e-11 relative error = 2.7764249417700829120790533599049e-09 % glob_h = 0.01 y2(analytic)= = -0.69122677159712679174928270996945 y2(numeric) = = -0.69122677158017767890641561798971 absolute error = 1.694911284286709197974e-11 relative error = 2.4520336218611738752963655095860e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.53 y1(analytic)= = 0.72951393178823184359114822234548 y1(numeric) = = 0.72951393176796253087368235863762 absolute error = 2.026931271746586370786e-11 relative error = 2.7784682148263310511804806158827e-09 % glob_h = 0.01 y2(analytic)= = -0.68396595187690082623325214965746 y2(numeric) = = -0.68396595186012229279376791092016 absolute error = 1.677853343948423873730e-11 relative error = 2.4531240763434981931311123271548e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.54 y1(analytic)= = 0.7363170019206192227470992412368 y1(numeric) = = 0.73631700190014550543908027863926 absolute error = 2.047371730801896259754e-11 relative error = 2.7805574575373163418134160760610e-09 % glob_h = 0.01 y2(analytic)= = -0.67663673613145689729665309019517 y2(numeric) = = -0.67663673611485136765515841483401 absolute error = 1.660552964149467536116e-11 relative error = 2.4541277105989934334734638806685e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.55 y1(analytic)= = 0.7430464409664099962599385961293 y1(numeric) = = 0.74304644094573331122879758741839 absolute error = 2.067668503114100871091e-11 relative error = 2.7826908105836300827204132104148e-09 % glob_h = 0.01 y2(analytic)= = -0.66923985727626188990340552174474 y2(numeric) = = -0.66923985725983177729667669551349 absolute error = 1.643011260672882623125e-11 relative error = 2.4550409584984541172358013099862e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.56 y1(analytic)= = 0.74970157598730743223095445615738 y1(numeric) = = 0.74970157596642924419810078601955 absolute error = 2.087818803285367013783e-11 relative error = 2.7848664990944531781943338980226e-09 % glob_h = 0.01 y2(analytic)= = -0.66177605499303727838843528095042 y2(numeric) = = -0.66177605497678498457882736086057 absolute error = 1.625229380960792008985e-11 relative error = 2.4558600582456726677539363898396e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.57 y1(analytic)= = 0.75628174147535536828084442543044 y1(numeric) = = 0.75628174145427716973548737400186 absolute error = 2.107819854535705142858e-11 relative error = 2.7870828276559573304419961534353e-09 % glob_h = 0.01 y2(analytic)= = -0.6542460756557915707096204525212 y2(numeric) = = -0.65424607563971948566901718648965 absolute error = 1.607208504060326603155e-11 relative error = 2.4565810386395080249432542946482e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=148.7MB, alloc=4.4MB, time=8.09 x[1] = = 5.58 y1(analytic)= = 0.76278627941948845257783863453346 y1(numeric) = = 0.76278627939821176368727042367358 absolute error = 2.127668889056821085988e-11 relative error = 2.7893381756631282180716610761772e-09 % glob_h = 0.01 y2(analytic)= = -0.64665067225618352957326274728807 y2(numeric) = = -0.64665067224029403116760641006096 absolute error = 1.588949840565633722711e-11 relative error = 2.4571997041644451111492472121861e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.59 y1(analytic)= = 0.7692145393713327020321562629051 y1(numeric) = = 0.76921453934985907054849960380199 absolute error = 2.147363148365665910311e-11 relative error = 2.7916309929875649823205123045260e-09 % glob_h = 0.01 y2(analytic)= = -0.63899060432822363404877420119334 y2(numeric) = = -0.63899060431251908772321454073258 absolute error = 1.570454632555966046076e-11 relative error = 2.4577116187913257752885759888056e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.6 y1(analytic)= = 0.77556587851024979765580966215728 y1(numeric) = = 0.7755658784885807988192332531804 absolute error = 2.166899883657640897688e-11 relative error = 2.7939597959362821234807403320356e-09 % glob_h = 0.01 y2(analytic)= = -0.63126663787232131146366915371667 y2(numeric) = = -0.63126663785680406992837063947195 absolute error = 1.551724153529851424472e-11 relative error = 2.4581120883560774396390727382726e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.61 y1(analytic)= = 0.7818396617076186127124234987124 y1(numeric) = = 0.78183966168575584915082935298845 absolute error = 2.186276356159414572395e-11 relative error = 2.7963231634787637803891631312230e-09 % glob_h = 0.01 y2(analytic)= = -0.62347954527868553479237824409858 y2(numeric) = = -0.62347954526335793770902480113434 absolute error = 1.532759708335344296424e-11 relative error = 2.4583961413685590166958629281499e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.62 y1(analytic)= = 0.78803526159034754555782169540902 y1(numeric) = = 0.78803526156829264718300860834919 absolute error = 2.205489837481308705983e-11 relative error = 2.7987197337215236368417506897471e-09 % glob_h = 0.01 y2(analytic)= = -0.61563010525008644541531292122822 y2(numeric) = = -0.61563010523495081908434932202676 absolute error = 1.513562633096359920146e-11 relative error = 2.4585585080858054562053069878582e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.63 y1(analytic)= = 0.79415205860361130599102488099306 y1(numeric) = = 0.79415205858136592989133277889309 absolute error = 2.224537609969210209997e-11 relative error = 2.8011482006112304079071540398537e-09 % glob_h = 0.01 y2(analytic)= = -0.60771910272398572502153946092775 y2(numeric) = = -0.60771910270904438207018852984188 absolute error = 1.494134295135093108587e-11 relative error = 2.4585935976636561939913529055210e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.64 y1(analytic)= = 0.80018944107280588148930372877341 y1(numeric) = = 0.8001894410503717118187440705915 absolute error = 2.243416967055965818191e-11 relative error = 2.8036073108490901925994992219155e-09 % glob_h = 0.01 y2(analytic)= = -0.5997473287940435035529810827878 y2(numeric) = = -0.59974732877929874262407584656554 absolute error = 1.474476092890523622226e-11 relative error = 2.4584954731776166633207596961215e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.65 y1(analytic)= = 0.80614680526471548788229364554041 y1(numeric) = = 0.80614680524209423574617148098071 absolute error = 2.262125213612216455970e-11 relative error = 2.8060958610006516382344623288922e-09 % glob_h = 0.01 y2(analytic)= = -0.59171558063100965243394305433196 y2(numeric) = = -0.59171558061646375787561294587769 absolute error = 1.454589455833010845427e-11 relative error = 2.4582578242773773679184027011673e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.66 y1(analytic)= = 0.81202355544788538782107568826578 y1(numeric) = = 0.81202355542507879115810940630561 absolute error = 2.280659666296628196017e-11 relative error = 2.8086126947865343758080226715327e-09 % glob_h = 0.01 y2(analytic)= = -0.5836246614030073738907141274371 y2(numeric) = = -0.58362466138866261544696431900601 absolute error = 1.434475844374980843109e-11 relative error = 2.4578739372091741036280520600989e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.67 y1(analytic)= = 0.81781910395219453981068731484753 y1(numeric) = = 0.81781910392920436327163254779449 absolute error = 2.299017653905476705304e-11 relative error = 2.8111567005407901855978438319163e-09 % glob_h = 0.01 y2(analytic)= = -0.57547538019521705793588222606621 y2(numeric) = = -0.5754753801810756904381051324092 absolute error = 1.414136749777709365701e-11 relative error = 2.4573366619054933891452104573090e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.68 y1(analytic)= = 0.82353287122762212059080342653966 y1(numeric) = = 0.82353287120445015541358800553782 absolute error = 2.317196517721542100184e-11 relative error = 2.8137268088247028055740193994335e-09 % glob_h = 0.01 y2(analytic)= = -0.56726855192896843856473605766545 y2(numeric) = = -0.56726855191503270162419400924787 absolute error = 1.393573694054204841758e-11 relative error = 2.4566383758017731634680687864235e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.69 y1(analytic)= = 0.82916428590220204426132157270589 y1(numeric) = = 0.82916428587885010814269886127857 absolute error = 2.335193611862271142732e-11 relative error = 2.8163219901848277098538256633434e-09 % glob_h = 0.01 y2(analytic)= = -0.55900499728024913988071002963799 y2(numeric) = = -0.55900499726652125758202807094698 absolute error = 1.372788229868195869101e-11 relative error = 2.4557709439938480090235844051057e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.7 y1(analytic)= = 0.83471278483915968274923403099742 y1(numeric) = = 0.83471278481562961971296239366503 absolute error = 2.353006303627163733239e-11 relative error = 2.8189412530449777868084600829127e-09 % glob_h = 0.01 y2(analytic)= = -0.55068554259763776122735060787247 y2(numeric) = = -0.55068554258411994182305832600298 absolute error = 1.351781940429228186949e-11 relative error = 2.4547256752969037090450108142749e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.71 y1(analytic)= = 0.84017781319322507399235385075605 y1(numeric) = = 0.84017781316951875425391044395109 absolute error = 2.370631973844340680496e-11 relative error = 2.8215836417226837345067087573166e-09 % glob_h = 0.01 y2(analytic)= = -0.54231101981966970794990205292996 y2(numeric) = = -0.54231101980636414355606328709913 absolute error = 1.330556439383876583083e-11 relative error = 2.4534932737054020065335313340643e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=152.5MB, alloc=4.4MB, time=8.29 x[1] = = 5.72 y1(analytic)= = 0.84555882446611698656600400409952 y1(numeric) = = 0.84555882444223630639384150646486 absolute error = 2.388068017216249763466e-11 relative error = 2.8242482345614072700610596454823e-09 % glob_h = 0.01 y2(analytic)= = -0.53388226639164403113457379715617 y2(numeric) = = -0.53388226637855289742754302053956 absolute error = 1.309113370703077661661e-11 relative error = 2.4520637846823357800555046460931e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.73 y1(analytic)= = 0.8508552805611922923924435421742 y1(numeric) = = 0.85085528053713917396579887082412 absolute error = 2.405311842664467135008e-11 relative error = 2.8269341421704681474397021751793e-09 % glob_h = 0.01 y2(analytic)= = -0.52540012518187959557218813352221 y2(numeric) = = -0.5254001251690050514865322348349 absolute error = 1.287454408565589868731e-11 relative error = 2.4504265356235065255312578673346e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.74 y1(analytic)= = 0.85606665183725518264130080608025 y1(numeric) = = 0.85606665181303157390456529447569 absolute error = 2.422360873673551160456e-11 relative error = 2.8296405057652689498265211114613e-09 % glob_h = 0.01 y2(analytic)= = -0.51686544439742895025962555734949 y2(numeric) = = -0.51686544438477313768724968091128 absolute error = 1.265581257237587643821e-11 relative error = 2.4485700697461504340086030154548e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.75 y1(analytic)= = 0.86119241716152084594426451292894 y1(numeric) = = 0.86119241713712872045792545461657 absolute error = 2.439212548633905831237e-11 relative error = 2.8323664956009704377637817759228e-09 % glob_h = 0.01 y2(analytic)= = -0.50827907749925832998177940926343 y2(numeric) = = -0.50827907748682337347229543889283 absolute error = 1.243495650948397037060e-11 relative error = 2.4464820725386075319287877979520e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.76 y1(analytic)= = 0.86623206396172831260034749931466 y1(numeric) = = 0.8662320639371696693885113898533 absolute error = 2.455864321183610946136e-11 relative error = 2.8351113094932900566425426734242e-09 % glob_h = 0.01 y2(analytic)= = -0.49964188311690226990317852750738 y2(numeric) = = -0.49964188310469027636555472148614 absolute error = 1.221199353762380602124e-11 relative error = 2.4441492897757212282521490112109e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.77 y1(analytic)= = 0.87118508827739725353072982124056 y1(numeric) = = 0.87118508825267411692523805813661 absolute error = 2.472313660549176310395e-11 relative error = 2.8378741714205716631563118091957e-09 % glob_h = 0.01 y2(analytic)= = -0.49095472496260136763669782991456 y2(numeric) = = -0.49095472495061442604222803145655 absolute error = 1.198694159446979845801e-11 relative error = 2.4415574359494976950103941860408e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.78 y1(analytic)= = 0.87605099481022360834599958293728 y1(numeric) = = 0.87605099478533802782714781028137 absolute error = 2.488558051885177265591e-11 relative error = 2.8406543302017097695471390895196e-09 % glob_h = 0.01 y2(analytic)= = -0.48221847174493177894159832804301 y2(numeric) = = -0.48221847173317196002822908819164 absolute error = 1.175981891336923985137e-11 relative error = 2.4386910917816449462531487886285e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.79 y1(analytic)= = 0.88082929697360900300498098722694 y1(numeric) = = 0.88082929694856305303885369791638 absolute error = 2.504594996612728931056e-11 relative error = 2.8434510582449103522377787815221e-09 % glob_h = 0.01 y2(analytic)= = -0.47343399708193508402935158913795 y2(numeric) = = -0.47343399707040444000740544681012 absolute error = 1.153064402194614232783e-11 relative error = 2.4355335892683232537058204850983e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.8 y1(analytic)= = 0.88551951694131900416465810176149 y1(numeric) = = 0.88551951691611478403709053565564 absolute error = 2.520422012756756610585e-11 relative error = 2.8462636503626358762663103049633e-09 % glob_h = 0.01 y2(analytic)= = -0.46460217941375721141822652670259 y2(numeric) = = -0.46460217940245777567755959369826 absolute error = 1.129943574066693300433e-11 relative error = 2.4320668824508636003782301400060e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.81 y1(analytic)= = 0.89012118569526534443630775888889 y1(numeric) = = 0.89012118566990497808348755992599 absolute error = 2.536036635282019896290e-11 relative error = 2.8490914226484176612331924334794e-09 % glob_h = 0.01 y2(analytic)= = -0.45572390191480515537145240687951 y2(numeric) = = -0.45572390190373894219008430409066 absolute error = 1.106621318136810278885e-11 relative error = 2.4282714018008352866191504398171e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.82 y1(analytic)= = 0.89463384307240734036513436417581 y1(numeric) = = 0.89463384304689297620085588332897 absolute error = 2.551436416427848084684e-11 relative error = 2.8519337114115267711183878148646e-09 % glob_h = 0.01 y2(analytic)= = -0.44680005240543027117401176288256 y2(numeric) = = -0.44680005239459927542826584766905 absolute error = 1.083099574574591521351e-11 relative error = 2.4241258897431316872642162989729e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.83 y1(analytic)= = 0.89905703781076781303069303480741 y1(numeric) = = 0.89905703778510162377027758872341 absolute error = 2.566618926041544608400e-11 relative error = 2.8547898721657776947937738904919e-09 % glob_h = 0.01 y2(analytic)= = -0.43783152326314697984493852957562 y2(numeric) = = -0.4378315232525531767211302433348 absolute error = 1.059380312380828624082e-11 relative error = 2.4196072144036012984854625684280e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.84 y1(analytic)= = 0.90339032759455890971438749822898 y1(numeric) = = 0.90339032756874309219528331542487 absolute error = 2.581581751910418280411e-11 relative error = 2.8576592786689994029019049702641e-09 % glob_h = 0.01 y2(analytic)= = -0.42881921133339576034066600225909 y2(numeric) = = -0.42881921132304110504837705160851 absolute error = 1.035465529228895065058e-11 relative error = 2.4146901581418366160773038470950e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.85 y1(analytic)= = 0.90763327909841331408948072727997 y1(numeric) = = 0.90763327907245008908855673481803 absolute error = 2.596322500092399246194e-11 relative error = 2.8605413220099479126801569899663e-09 % glob_h = 0.01 y2(analytic)= = -0.41976401783985935287584035958477 y2(numeric) = = -0.41976401782974578036281632430976 absolute error = 1.011357251302403527501e-11 relative error = 2.4093471767945530375108206359152e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.86 y1(analytic)= = 0.91178546803071642184945852971753 y1(numeric) = = 0.91178546800460803389700655328847 absolute error = 2.610838795245197642906e-11 relative error = 2.8634354097396550664500825554785e-09 % glob_h = 0.01 y2(analytic)= = -0.4106668482943411416665314211351 y2(numeric) = = -0.41066684828447056633524025713465 absolute error = 9.87057533129116400045e-12 relative error = 2.4035481247847240421642547554262e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=8.52 NO POLE NO POLE x[1] = = 5.87 y1(analytic)= = 0.9158464791760351485932932817607 y1(numeric) = = 0.91584647914978386578375365102651 absolute error = 2.625128280953963073419e-11 relative error = 2.8663409650444114615833592826325e-09 % glob_h = 0.01 y2(analytic)= = -0.40152861240621472918246522121463 y2(numeric) = = -0.40152861239658904460835399711751 absolute error = 9.62568457411122409712e-12 relative error = 2.3972599403135936730644261180614e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.88 y1(analytic)= = 0.91981590643663912712217650132867 y1(numeric) = = 0.91981590641024724092160247015974 absolute error = 2.639188620057403116893e-11 relative error = 2.8692574259577688352499275471258e-09 % glob_h = 0.01 y2(analytic)= = -0.39235022399145375687539473900155 y2(numeric) = = -0.39235022398207483552688181093025 absolute error = 9.37892134851292807130e-12 relative error = 2.3904462837052493749738605593812e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.89 y1(analytic)= = 0.92369335287311014206259147012663 y1(numeric) = = 0.92369335284657996711286827796187 absolute error = 2.653017494972319216476e-11 relative error = 2.8721842446091200433749513768171e-09 % glob_h = 0.01 y2(analytic)= = -0.3831326008812510693257277179545 y2(numeric) = = -0.38313260087212076228596740809641 absolute error = 9.13030703976030985809e-12 relative error = 2.3830671205633520549740823527344e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.9 y1(analytic)= = 0.92747843074403574090610468003246 y1(numeric) = = 0.92747843071736961482593949594512 absolute error = 2.666612608016518408734e-11 relative error = 2.8751208865065742927816278059238e-09 % glob_h = 0.01 y2(analytic)= = -0.37387666483023635981484646898338 y2(numeric) = = -0.37387666482135649650530317019769 absolute error = 8.87986330954329878569e-12 relative error = 2.3750782396583424275969367849924e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.91 y1(analytic)= = 0.93117076154478305213785002357954 y1(numeric) = = 0.93117076151798333532054942869527 absolute error = 2.679971681730059488427e-11 relative error = 2.8780668298519925891482380734288e-09 % glob_h = 0.01 y2(analytic)= = -0.36458334142430147548207738499803 y2(numeric) = = -0.36458334141567386338794586565368 absolute error = 8.62761209413151934435e-12 relative error = 2.3664306933022260598593563868077e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.92 y1(analytic)= = 0.9347699760453489331042042875189 y1(numeric) = = 0.934769976018418008512256364155 absolute error = 2.693092459194792336390e-11 relative error = 2.8810215648861844511918796044020e-09 % glob_h = 0.01 y2(analytic)= = -0.35525355998804259945898248022107 y2(numeric) = = -0.35525355997966902385649101083746 absolute error = 8.37357560249146938361e-12 relative error = 2.3570701452712574370578658736523e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.93 y1(analytic)= = 0.93827571432728266263640886666204 y1(numeric) = = 0.93827571430022293559288737388799 absolute error = 2.705972704352149277405e-11 relative error = 2.8839845932623927221457460412727e-09 % glob_h = 0.01 y2(analytic)= = -0.34588825349182856568562826732762 y2(numeric) = = -0.34588825348371078937126103338747 absolute error = 8.11777631436723394015e-12 relative error = 2.3469361079528571740328383780675e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.94 y1(analytic)= = 0.94168762581967748619164414378966 y1(numeric) = = 0.94168762579249138416845266899858 absolute error = 2.718610202319147479108e-11 relative error = 2.8869554274463096099319404753795e-09 % glob_h = 0.01 y2(analytic)= = -0.33648835845850459949990753268065 y2(numeric) = = -0.33648835845064436252158263621648 absolute error = 7.86023697832489646417e-12 relative error = 2.3359610461216633311206616133409e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.95 y1(analytic)= = 0.94500536933422741438703528249648 y1(numeric) = = 0.94500536930691738679000966697426 absolute error = 2.731002759702561552222e-11 relative error = 2.8899335901409746600486667504596e-09 % glob_h = 0.01 y2(analytic)= = -0.32705481486974081354810845379823 y2(numeric) = = -0.32705481486213983293834764003303 absolute error = 7.60098060976081376520e-12 relative error = 2.3240693193243852878698507335472e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.96 y1(analytic)= = 0.94822861309934576927594993379112 y1(numeric) = = 0.94822861307191428722683767712559 absolute error = 2.743148204911225666553e-11 relative error = 2.8929186137350048953002658194774e-09 % glob_h = 0.01 y2(analytic)= = -0.31758856607203482408909734220883 y2(numeric) = = -0.31758856606469479360022341667174 absolute error = 7.34003048887392553709e-12 relative error = 2.3111759279170881810100689636730e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.97 y1(analytic)= = 0.9513570347933420665403922538039 y1(numeric) = = 0.95135703476579162265572800723964 absolute error = 2.755044388466424656426e-11 relative error = 2.8959100397726994689542150162908e-09 % glob_h = 0.01 y2(analytic)= = -0.30809055868237788735215370144406 y2(numeric) = = -0.30809055867530047719355142759717 absolute error = 7.07741015860227384689e-12 relative error = 2.2971850188692868823846223833478e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.98 y1(analytic)= = 0.95439032157665391593892130286986 y1(numeric) = = 0.95439032154898702410581796533584 absolute error = 2.766689183310333753402e-11 relative error = 2.8989074184446464421043782653204e-09 % glob_h = 0.01 y2(analytic)= = -0.29856174249359398925621052566581 y2(numeric) = = -0.29856174248678084583368661318384 absolute error = 6.81314342252391248197e-12 relative error = 2.2819880958693483256862313172337e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 5.99 y1(analytic)= = 0.95732817012313071684690886165419 y1(numeric) = = 0.95732817009534991199578419412135 absolute error = 2.778080485112466753284e-11 relative error = 2.9019103080975382316625196185803e-09 % glob_h = 0.01 y2(analytic)= = -0.28900307037936135450264408594397 y2(numeric) = = -0.28900307037281410015992169539918 absolute error = 6.54725434272239054479e-12 relative error = 2.2654618631311092076201776127876e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6 y1(analytic)= = 0.96017028665036602054565229792292 y1(numeric) = = 0.96017028662247385841991137193797 absolute error = 2.789216212574092598495e-11 relative error = 2.9049182747619753566584670461775e-09 % glob_h = 0.01 y2(analytic)= = -0.27941549819892587281155544661189 y2(numeric) = = -0.27941549819264610557393844744887 absolute error = 6.27976723761699916302e-12 relative error = 2.2474656123570527850603202425105e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.4MB, time=8.74 NO POLE x[1] = = 6.01 y1(analytic)= = 0.9629163869490755260493904569901 y1(numeric) = = 0.96291638692107458297208465163029 absolute error = 2.800094307730580535981e-11 relative error = 2.9079308916971057705401809129774e-09 % glob_h = 0.01 y2(analytic)= = -0.26979998470151597087951487009622 y2(numeric) = = -0.26979998469550526419975689545078 absolute error = 6.01070667975797464544e-12 relative error = 2.2278380357981544650452843080728e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.02 y1(analytic)= = 0.96556619641151777169512145583622 y1(numeric) = = 0.9655661963834106443326051138886 absolute error = 2.810712736251634194762e-11 relative error = 2.9109477389510097013668945586527e-09 % glob_h = 0.01 y2(analytic)= = -0.26015749143046848849191932792558 y2(numeric) = = -0.26015749142472839099833247206666 absolute error = 5.74009749358685585892e-12 relative error = 2.2063933127680063286206804069612e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.03 y1(analytic)= = 0.96811945005895468044974722983034 y1(numeric) = = 0.96811945003074398557235347866934 absolute error = 2.821069487739375116100e-11 relative error = 2.9139684029357978915352436703202e-09 % glob_h = 0.01 y2(analytic)= = -0.25048898262707514612245704524404 y2(numeric) = = -0.25048898262160718136929484721395 absolute error = 5.46796475316219803009e-12 relative error = 2.1829162687377892925332822318815e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.04 y1(analytic)= = 0.97057589256814921290289782907821 y1(numeric) = = 0.97057589253983758714265546444763 absolute error = 2.831162576024236463058e-11 relative error = 2.9169924760164447642859666599845e-09 % glob_h = 0.01 y2(analytic)= = -0.24079542513415921929279145580043 y2(numeric) = = -0.24079542512896488551294060621564 absolute error = 5.19433377985084958479e-12 relative error = 2.1571563400578833588899747932651e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.05 y1(analytic)= = 0.97293527829689747820221748585607 y1(numeric) = = 0.9729352782684875778076312075078 absolute error = 2.840990039458627834827e-11 relative error = 2.9200195561124276473363336443442e-09 % glob_h = 0.01 y2(analytic)= = -0.23107778829939206194467609549304 y2(numeric) = = -0.23107778829447283180469109246345 absolute error = 4.91923013998500302959e-12 relative error = 2.1288199857666479735875230291047e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.06 y1(analytic)= = 0.97519737130859274974129561271392 y1(numeric) = = 0.97519737128008725032921228956667 absolute error = 2.850549941208332314725e-11 relative error = 2.9230492463112890305121399125505e-09 % glob_h = 0.01 y2(analytic)= = -0.22133704387835914709159392768868 y2(numeric) = = -0.22133704387371646744910869243665 absolute error = 4.64267964248523525203e-12 relative error = 2.0975610594296752309544964041640e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.07 y1(analytic)= = 0.97736194539581892921914388298845 y1(numeric) = = 0.97736194536722052552372791209754 absolute error = 2.859840369541597089091e-11 relative error = 2.9260811544932811761063125094795e-09 % glob_h = 0.01 y2(analytic)= = -0.21157416593738531806507790618705 y2(numeric) = = -0.21157416593302060972862814921873 absolute error = 4.36470833644975696832e-12 relative error = 2.0629684711797366200970476928495e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.08 y1(analytic)= = 0.97942878410297109974447460052972 y1(numeric) = = 0.97942878407428250536331580865527 absolute error = 2.868859438115879187445e-11 relative error = 2.9291148929662914681485835908654e-09 % glob_h = 0.01 y2(analytic)= = -0.20179013075612896774960945640875 y2(numeric) = = -0.2017901307520436252408993610289 absolute error = 4.08534250871009537985e-12 relative error = 2.0245502063960634757779567885942e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.09 y1(analytic)= = 0.98139768074790090594832032889023 y1(numeric) = = 0.98139768071912485308569824776775 absolute error = 2.877605286262208112248e-11 relative error = 2.9321500781102828900643836964092e-09 % glob_h = 0.01 y2(analytic)= = -0.19198591672995488630700013822577 y2(numeric) = = -0.1919859167261502776256466998147 absolute error = 3.80460868135343841107e-12 relative error = 1.9817123808643505153783700635304e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.1 y1(analytic)= = 0.98326843844258459658502127464799 y1(numeric) = = 0.98326843841372383579235000115477 absolute error = 2.886076079267127349322e-11 relative error = 2.9351863300305171511501058176581e-09 % glob_h = 0.01 y2(analytic)= = -0.18216250427209554002412836322466 y2(numeric) = = -0.18216250426857300641491649003262 absolute error = 3.52253360921187319204e-12 relative error = 1.9337314357241577000885003485084e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.11 y1(analytic)= = 0.98504087011281166283454363754829 y1(numeric) = = 0.98504087008386896274802186777352 absolute error = 2.894270008652176977477e-11 relative error = 2.9382232722188584158531783730338e-09 % glob_h = 0.01 y2(analytic)= = -0.17232087571561056507461439687741 y2(numeric) = = -0.17232087571237142079729564116025 absolute error = 3.23914427731875571716e-12 relative error = 1.8797166993652419783908950013075e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.12 y1(analytic)= = 0.98671479851689210345870583952381 y1(numeric) = = 0.98671479848787025053419704124271 absolute error = 2.902185292450879828110e-11 relative error = 2.9412605312224834853508905915299e-09 % glob_h = 0.01 y2(analytic)= = -0.16246201521515428016335732858881 y2(numeric) = = -0.16246201521219981226502487573067 absolute error = 2.95446789833245285814e-12 relative error = 1.8185591840774256901181426390507e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.13 y1(analytic)= = 0.98829005626338044610038634563587 y1(numeric) = = 0.98829005623428224434555440681088 absolute error = 2.909820175483193882499e-11 relative error = 2.9442977363193497833341064856595e-09 % glob_h = 0.01 y2(analytic)= = -0.15258690864856104122080942266136 y2(numeric) = = -0.15258690864589250931088172052873 absolute error = 2.66853190992770213263e-12 relative error = 1.7488603272472598925312230622537e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.14 y1(analytic)= = 0.9897664858278147523383531246708 y1(numeric) = = 0.98976648579864302304207918630945 absolute error = 2.917172929627393836135e-11 relative error = 2.9473345191997957387548255971212e-09 % glob_h = 0.01 y2(analytic)= = -0.14269654351825827952950649169451 y2(numeric) = = -0.14269654351587691555735165286439 absolute error = 2.38136397215483883012e-12 relative error = 1.6688308724521691196766661804539e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=164.0MB, alloc=4.4MB, time=8.96 x[1] = = 6.15 y1(analytic)= = 0.99114393956846893261115839082715 y1(numeric) = = 0.99114393953922651407026494076977 absolute error = 2.924241854089345005738e-11 relative error = 2.9503705136536692568463191946240e-09 % glob_h = 0.01 y2(analytic)= = -0.13279190885251708189688611167219 y2(numeric) = = -0.1327919088504240899321189673989 absolute error = 2.09299196476714427329e-12 relative error = 1.5761441964748678534051436925153e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.16 y1(analytic)= = 0.99242227974111679579173312236649 y1(numeric) = = 0.99242227971180654303504179231098 absolute error = 2.931025275669133005551e-11 relative error = 2.9534053552623990336524736569649e-09 % glob_h = 0.01 y2(analytic)= = -0.12287399510655018773408548803084 y2(numeric) = = -0.12287399510474674374956891488632 absolute error = 1.80344398451657314452e-12 relative error = 1.4677181961510380216039495602036e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.17 y1(analytic)= = 0.99360137851280635702002723141034 y1(numeric) = = 0.99360137848343114152977710265945 absolute error = 2.937521549025012875089e-11 relative error = 2.9564386810954405955779109811732e-09 % glob_h = 0.01 y2(analytic)= = -0.11294379406346729315859303188137 y2(numeric) = = -0.11294379406195454481617490994636 absolute error = 1.51274834241812193501e-12 relative error = 1.3393815525340442508519798776537e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.18 y1(analytic)= = 0.99468111797464302637439067246476 y1(numeric) = = 0.99468111794520573580504425645809 absolute error = 2.943729056934641600667e-11 relative error = 2.9594701294105442209512634915094e-09 % glob_h = 0.01 y2(analytic)= = -0.10300229873509756650780640976964 y2(numeric) = = -0.10300229873387663294682330509446 absolute error = 1.22093356098310467518e-12 relative error = 1.1853459349709416701648756803581e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.19 y1(analytic)= = 0.99566139015358040007348097327921 y1(numeric) = = 0.99566139012408393796794539090135 absolute error = 2.949646210553558237786e-11 relative error = 2.9624993393573054028238274445062e-09 % glob_h = 0.01 y2(analytic)= = -0.093050503262689292929298082924481 y2(numeric) = = -0.093050503261761264557876476743215 absolute error = 9.28028371421606181266e-13 relative error = 9.9733836882290155066923694216725e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.2 y1(analytic)= = 0.99654209702321747513940262386926 y1(numeric) = = 0.99654209699366476064269386276191 absolute error = 2.955271449670876110735e-11 relative error = 2.9655259506834703097341939951111e-09 % glob_h = 0.01 y2(analytic)= = -0.083089402817496578000579289098367 y2(numeric) = = -0.083089402816862516289764901995862 absolute error = 6.34061710814387102505e-13 relative error = 7.6310779631800332508072716574128e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.21 y1(analytic)= = 0.99732315051360120780960965865819 y1(numeric) = = 0.99732315048399517537998814026234 absolute error = 2.960603242962151839585e-11 relative error = 2.9685496034434788541845152928197e-09 % glob_h = 0.01 y2(analytic)= = -0.07311999350126305162515635309984 y2(numeric) = = -0.073119993500923988905901834024115 absolute error = 3.39062719254519075725e-13 relative error = 4.6370726120026557938143420433734e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.22 y1(analytic)= = 0.99800447252003343544989901292626 y1(numeric) = = 0.99800447249037703456750505069609 absolute error = 2.965640088239396223017e-11 relative error = 2.9715699377087365392393585648911e-09 % glob_h = 0.01 y2(analytic)= = -0.063143272246612523751559750067066 y2(numeric) = = -0.0631432722465694630146007177774 absolute error = 4.3060736959032289666e-14 relative error = 6.8195288946784649542180685887409e-11 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.23 y1(analytic)= = 0.99858599491088128128364243136292 y1(numeric) = = 0.99858599488117747615666050848045 absolute error = 2.970380512698192288247e-11 relative error = 2.9745865932791132667055776304648e-09 % glob_h = 0.01 y2(analytic)= = -0.0531602367173565527667665083675 y2(numeric) = = -0.053160236717610467465415646638898 absolute error = 2.53914698649138271398e-13 relative error = 4.7764027086477661554510830380136e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.24 y1(analytic)= = 0.99906765953439026090329265444287 y1(numeric) = = 0.99906765950464203017167379337846 absolute error = 2.974823073161886106441e-11 relative error = 2.9775992093951727928637470535467e-09 % glob_h = 0.01 y2(analytic)= = -0.043171885208728895724099860467483 y2(numeric) = = -0.043171885209280729579988478163608 absolute error = 5.51833855888617696125e-13 relative error = 1.2782250606397951865730433041081e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.25 y1(analytic)= = 0.99944941822449940925919030184204 y1(numeric) = = 0.99944941819470974569596213920507 absolute error = 2.978966356322816263697e-11 relative error = 2.9806074244506405402442032449388e-09 % glob_h = 0.01 y2(analytic)= = -0.033179216547556816877445670789293 y2(numeric) = = -0.033179216548407483689241843797212 absolute error = 8.50666811796173007919e-13 relative error = 2.5638544254861637669661618746096e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.26 y1(analytic)= = 0.99973123280565784661781849520905 y1(numeric) = = 0.999731232775829756828013013473 absolute error = 2.982808978980548173605e-11 relative error = 2.9836108757046200396581309416203e-09 % glob_h = 0.01 y2(analytic)= = -0.023183229992379237307741919992809 y2(numeric) = = -0.023183229993529620762874034013328 absolute error = 1.150383455132114020519e-12 relative error = 4.9621362317082936553881689423917e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.27 y1(analytic)= = 0.99991307509664230183692318641599 y1(numeric) = = 0.9999130750667788059541523892383 absolute error = 2.986349588277079717769e-11 relative error = 2.9866091989930694026488056499059e-09 % glob_h = 0.01 y2(analytic)= = -0.013184925133521713743543998871196 y2(numeric) = = -0.013184925134972667232958210208052 absolute error = 1.450953489414211336856e-12 relative error = 1.1004639576794164415953401457536e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.28 y1(analytic)= = 0.99999492691337521120835293804732 y1(numeric) = = 0.999994926883479342589063087994 absolute error = 2.989586861928985005332e-11 relative error = 2.9896020284390489209117880314178e-09 % glob_h = 0.01 y2(analytic)= = -0.0031853017931382389945131819173505 y2(numeric) = = -0.0031853017948905854304930077373654 absolute error = 1.7523464359798258200149e-12 relative error = 5.5013513625450550579359336294031e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.29 y1(analytic)= = 0.99997678007074311106108228002322 y1(numeric) = = 0.99997678004081791597651764650834 absolute error = 2.992519508456463351488e-11 relative error = 2.9925889961612491599778867042484e-09 % glob_h = 0.01 y2(analytic)= = 0.0068146400747701402655132902638216 y2(numeric) = = 0.0068146400727156086284373501885471 absolute error = 2.0545316370759400752745e-12 relative error = 3.0148791638790108921289937523676e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=9.16 NO POLE NO POLE x[1] = = 6.3 y1(analytic)= = 0.99985863638341514228667366213969 y1(numeric) = = 0.9998586363534636796125810532579 absolute error = 2.995146267409260888179e-11 relative error = 2.9955697319803057571051655963039e-09 % glob_h = 0.01 y2(analytic)= = 0.016813900484349890310966367494096 y2(numeric) = = 0.016813900481992412051989588770455 absolute error = 2.357478258976778723641e-12 relative error = 1.4021007565562088268329951278051e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.31 y1(analytic)= = 0.99964050766566158493740754116133 y1(numeric) = = 0.99964050763568692584151321578509 absolute error = 2.997465909589432537624e-11 relative error = 2.9985438631224025390495752591353e-09 % glob_h = 0.01 y2(analytic)= = 0.026811479517892742399150869010765 y2(numeric) = = 0.026811479515231587104022168490346 absolute error = 2.661155295128700520419e-12 relative error = 9.9254324751186090109065526136934e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.32 y1(analytic)= = 0.9993224157301724410434695687937 y1(numeric) = = 0.9993224157001776686707604447843 absolute error = 2.999477237270912400940e-11 relative error = 3.0015110139196585289117362233423e-09 % glob_h = 0.01 y2(analytic)= = 0.036806377425826630335140406595538 y2(numeric) = = 0.036806377422861098765818364917767 absolute error = 2.965531569322041677771e-12 relative error = 8.0571134045948265016791588303572e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.33 y1(analytic)= = 0.99890439238587618378992865077926 y1(numeric) = = 0.99890439235586439294577004138007 absolute error = 3.001179084415860939919e-11 relative error = 3.0044708055067868909538122485547e-09 % glob_h = 0.01 y2(analytic)= = 0.046797594726689814556530565903147 y2(numeric) = = 0.046797594723419238817640979814897 absolute error = 3.270575738889586088250e-12 relative error = 6.9887688843638295650028008469646e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.34 y1(analytic)= = 0.99838647943475889117677047635081 y1(numeric) = = 0.99838647940473318800789289975133 absolute error = 3.002570316887757659948e-11 relative error = 3.0074228555135048398279358404210e-09 % glob_h = 0.01 y2(analytic)= = 0.056784132307078195408953363036756 y2(numeric) = = 0.056784132303501939111022028519271 absolute error = 3.576256297931334517485e-12 relative error = 6.2979852867903219013506862035921e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.35 y1(analytic)= = 0.99776872866768408224596980157531 y1(numeric) = = 0.99776872863764758391935771821449 absolute error = 3.003649832661208336082e-11 relative error = 3.0103667777521629810538517072947e-09 % glob_h = 0.01 y2(analytic)= = 0.06676499152155582096431457502319 y2(numeric) = = 0.066764991517673279383749333784166 absolute error = 3.882541580565241239024e-12 relative error = 5.8152356378443026631363615316325e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.36 y1(analytic)= = 0.99705120185921367388849532116029 y1(numeric) = = 0.99705120182916950826821095953699 absolute error = 3.004416562028436162330e-11 relative error = 3.0133021819000504108348580964812e-09 % glob_h = 0.01 y2(analytic)= = 0.076739174292518598414230599441425 y2(numeric) = = 0.076739174288329198650027016418273 absolute error = 4.189399764203583023152e-12 relative error = 5.4592713601975947208820535549070e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.37 y1(analytic)= = 0.99623397076143057613125057329467 y1(numeric) = = 0.99623397073138188145322630783103 absolute error = 3.004869467802426546364e-11 relative error = 3.0162286731758181363802915740793e-09 % glob_h = 0.01 y2(analytic)= = 0.086705683210001222750744981614211 y2(numeric) = = 0.086705683205504423877890359749313 absolute error = 4.496798872854621864898e-12 relative error = 5.1862792684112435697738488237073e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.38 y1(analytic)= = 0.99531711709676354363927436333187 y1(numeric) = = 0.99531711706671346818410740715272 absolute error = 3.005007545516695617915e-11 relative error = 3.0191458520094479260430016364851e-09 % glob_h = 0.01 y2(analytic)= = 0.09666352163141734212462870103641 y2(numeric) = = 0.096663521626612635344179481691634 absolute error = 4.804706780449219344776e-12 relative error = 4.9705480406246706217497447733894e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.39 y1(analytic)= = 0.99430073254981500094207121578889 y1(numeric) = = 0.99430073251976670270585468709713 absolute error = 3.004829823621652869176e-11 relative error = 3.0220533137051764975007570894613e-09 % glob_h = 0.01 y2(analytic)= = 0.10661169378122298594784491442111 y2(numeric) = = 0.10661169377610989473365285736162 absolute error = 5.11309121419205705949e-12 relative error = 4.7959947289502698658799560137906e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.4 y1(analytic)= = 0.99318491875819265859473909867216 y1(numeric) = = 0.99318491872814930495796381167675 absolute error = 3.004335363677528699541e-11 relative error = 3.0249506480967659292855210039490e-09 % glob_h = 0.01 y2(analytic)= = 0.11654920485049328948042048879895 y2(numeric) = = 0.11654920484507136972248337465948 absolute error = 5.42191975793711413947e-12 relative error = 4.6520435423752838224969512185956e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.41 y1(analytic)= = 0.99196978730234583710463801295928 y1(numeric) = = 0.99196978727231060449919963301143 absolute error = 3.003523260543837994785e-11 relative error = 3.0278374391944902547873449949408e-09 % glob_h = 0.01 y2(analytic)= = 0.12647506109640255731224596473812 y2(numeric) = = 0.12647506109067139745665891525222 absolute error = 5.73115985558704948590e-12 relative error = 4.5314545064489919148899703262386e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.42 y1(analytic)= = 0.9906554596944075149827370785494 y1(numeric) = = 0.99065545966438358855708356622377 absolute error = 3.002392642565351232563e-11 relative error = 3.0307132648231852782955430739156e-09 % glob_h = 0.01 y2(analytic)= = 0.13638826994159771781635554625737 y2(numeric) = = 0.13638826993555693900183941324479 absolute error = 6.04077881451613301258e-12 relative error = 4.4291043629359262646486737088144e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.43 y1(analytic)= = 0.98924206736604321670553671967699 y1(numeric) = = 0.98924206733603378998799126996157 absolute error = 3.000942671754544971542e-11 relative error = 3.0335776962506836392757528797882e-09 % glob_h = 0.01 y2(analytic)= = 0.14628784007345523131105272544038 y2(numeric) = = 0.14628784006710448750203635857283 absolute error = 6.35074380901636686755e-12 relative error = 4.3412656894978284685193260852537e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=9.37 NO POLE NO POLE x[1] = = 6.44 y1(analytic)= = 0.98772975165530795568864386462536 y1(numeric) = = 0.98772975162531623024893882511734 absolute error = 2.999172543970503950802e-11 relative error = 3.0364302978059299337190218676674e-09 % glob_h = 0.01 y2(analytic)= = 0.15617278154321152632277914361105 y2(numeric) = = 0.15617278153655050443901270927426 absolute error = 6.66102188376643433679e-12 relative error = 4.2651618405883312037539920784771e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.45 y1(analytic)= = 0.9861186637925125465667502912062 y1(numeric) = = 0.98611866376254173167580781721515 absolute error = 2.997081489094247399105e-11 relative error = 3.0392706264860411583175005537296e-09 % glob_h = 0.01 y2(analytic)= = 0.16604210586495705098870882370759 y2(numeric) = = 0.16604210585798547103138571280988 absolute error = 6.97157995732311089771e-12 relative error = 4.1986819674481452591051067411789e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.46 y1(analytic)= = 0.9844089648851007001370080863308 y1(numeric) = = 0.98440896485515401242500356102741 absolute error = 2.994668771200452530339e-11 relative error = 3.0420982315515457412140882549239e-09 % glob_h = 0.01 y2(analytic)= = 0.1758948261144840402764222822845 y2(numeric) = = 0.17589482610720165545078751359091 absolute error = 7.28238482563476869359e-12 relative error = 4.1401927427330402353495001912714e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.47 y1(analytic)= = 0.98260082590153841324370550325453 y1(numeric) = = 0.98260082587161907635645001743653 absolute error = 2.991933688725548581800e-11 relative error = 3.0449126541089998160228416316562e-09 % glob_h = 0.01 y2(analytic)= = 0.18572995702797811432631141850448 y2(numeric) = = 0.18572995702038471116073481596147 absolute error = 7.59340316557660254301e-12 relative error = 4.0884105542719435206711501569127e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.48 y1(analytic)= = 0.98069442765421726465182928523087 y1(numeric) = = 0.980694427624328508905507733872 absolute error = 2.988875574632155135887e-11 relative error = 3.0477134266801420239351110511290e-09 % glob_h = 0.01 y2(analytic)= = 0.1955465151005438388391236641071 y2(numeric) = = 0.19554651509263923730061646162728 absolute error = 7.90460153850720247982e-12 relative error = 4.0423126612319867486962988430728e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.49 y1(analytic)= = 0.97868996078137332656567889339494 y1(numeric) = = 0.97868996075151838859998050486116 absolute error = 2.985493796569838853378e-11 relative error = 3.0505000727567078177028052052492e-09 % glob_h = 0.01 y2(analytic)= = 0.20534351868455439503471099991399 y2(numeric) = = 0.20534351867633844864086490517313 absolute error = 8.21594639384609474086e-12 relative error = 4.0010741251917998055643126827378e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.5 y1(analytic)= = 0.97658762572802349988631325394407 y1(numeric) = = 0.97658762569820562231599162256983 absolute error = 2.981787757032163137424e-11 relative error = 3.0532721063399808004541441514925e-09 % glob_h = 0.01 y2(analytic)= = 0.21511998808781552429694574907473 y2(numeric) = = 0.21511998807928812022427387899475 absolute error = 8.52740407267187007998e-12 relative error = 3.9640221945302652241715227576935e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.51 y1(analytic)= = 0.97438763272592117955841794561013 y1(numeric) = = 0.97438763269614361062331788918981 absolute error = 2.977756893510005642032e-11 relative error = 3.0560290314641118543536709967441e-09 % glob_h = 0.01 y2(analytic)= = 0.22487494567153393119214167000114 y2(numeric) = = 0.22487494566269499038080115471222 absolute error = 8.83894081134051528892e-12 relative error = 3.9306027556538964731400994821489e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.52 y1(analytic)= = 0.97209020177253325442335458417224 y1(numeric) = = 0.97209020174279924763694339480498 absolute error = 2.973400678641118936726e-11 relative error = 3.0587703417021864724230190439442e-09 % glob_h = 0.01 y2(analytic)= = 0.23460741594808034810231857059532 y2(numeric) = = 0.23460741593892982535719500974699 absolute error = 9.15052274512356084833e-12 relative error = 3.9003552842287865847661052213590e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.53 y1(analytic)= = 0.96969556260904054386088799067957 y1(numeric) = = 0.96969556257935335765732889027439 absolute error = 2.968718620355910040518e-11 relative error = 3.0614955196539665551241084372148e-09 % glob_h = 0.01 y2(analytic)= = 0.24431642567853748524831606627424 y2(numeric) = = 0.24431642566907536933645041155784 absolute error = 9.46211591186565471640e-12 relative error = 3.8728938857003240523158558785474e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.54 y1(analytic)= = 0.96720395469736387115759406231192 y1(numeric) = = 0.96720395466772676853739991288143 absolute error = 2.963710262019414943049e-11 relative error = 3.0642040364141747028036713424472e-09 % glob_h = 0.01 y2(analytic)= = 0.2540010039700231113890438578016 y2(numeric) = = 0.2540010039602494251333826884136 absolute error = 9.77368625566116938800e-12 relative error = 3.8478927653430251465210423573977e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.55 y1(analytic)= = 0.96461562719621807097546663004764 y1(numeric) = = 0.96461562716663431914977218365918 absolute error = 2.958375182569444638846e-11 relative error = 3.0668953510201264334122219101386e-09 % glob_h = 0.01 y2(analytic)= = 0.26366018237277853296990090080709 y2(numeric) = = 0.26366018236269333333935145428221 absolute error = 1.008519963054944652488e-11 relative error = 3.8250749657338809629655413688633e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.56 y1(analytic)= = 0.96193083893619632550002151519356 y1(numeric) = = 0.96193083890666919553351271907355 absolute error = 2.952712996650879612001e-11 relative error = 3.0695689098774484634046279020277e-09 % glob_h = 0.01 y2(analytic)= = 0.27329299497701276295335542134344 y2(numeric) = = 0.27329299496661614114912714067577 absolute error = 1.039662180422828066767e-11 relative error = 3.8042035453937492815673956244384e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.57 y1(analytic)= = 0.95914985839388732081351999037144 y1(numeric) = = 0.95914985836442008726605908913993 absolute error = 2.946723354746090123151e-11 relative error = 3.0722241461625488613484521694308e-09 % glob_h = 0.01 y2(analytic)= = 0.28289847850949269499550592449408 y2(numeric) = = 0.28289847849878477653372068370114 absolute error = 1.070791846178524079294e-11 relative error = 3.7850746028052374999052324244698e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=175.4MB, alloc=4.4MB, time=9.56 x[1] = = 6.58 y1(analytic)= = 0.95627296366502781175610535815565 y1(numeric) = = 0.95627296363562375232309075747185 absolute error = 2.940405943301460068380e-11 relative error = 3.0748604792004271404272782149464e-09 % glob_h = 0.01 y2(analytic)= = 0.29247567242986962403169708343874 y2(numeric) = = 0.29247567241885056882225065766412 absolute error = 1.101905520944642577462e-11 relative error = 3.7675117105982877608093779921969e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.59 y1(analytic)= = 0.95330044243669327999599374566492 y1(numeric) = = 0.95330044240735567514749381965847 absolute error = 2.933760484849992600645e-11 relative error = 3.0774773138163287858428237482989e-09 % glob_h = 0.01 y2(analytic)= = 0.30202361902673248069940378030301 y2(numeric) = = 0.30202361901540248312106153315471 absolute error = 1.132999757834224714830e-11 relative error = 3.7513614381726268818319227020225e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.6 y1(analytic)= = 0.9502325919585294662197377216682 y1(numeric) = = 0.95023259192926159883843796038572 absolute error = 2.926786738129976128248e-11 relative error = 3.0800740396596588667160921580096e-09 % glob_h = 0.01 y2(analytic)= = 0.31154136351337817435498510559259 y2(numeric) = = 0.31154136350173746332669527563252 absolute error = 1.164071102828982996007e-11 relative error = 3.7364897222676358512724224319839e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.61 y1(analytic)= = 0.94706971901302765326537006658066 y1(numeric) = = 0.94706971898383280828337316926065 absolute error = 2.919484498199689732001e-11 relative error = 3.0826500304984727700550453729410e-09 % glob_h = 0.01 y2(analytic)= = 0.32102795412328946772981499396496 y2(numeric) = = 0.32102795411133830677822337405577 absolute error = 1.195116095159161990919e-11 relative error = 3.7227789038588912459207623764341e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.62 y1(analytic)= = 0.94381213988484667264534386615219 y1(numeric) = = 0.9438121398557281366798625914246 absolute error = 2.911853596548127472759e-11 relative error = 3.0852046434827581821802750098144e-09 % glob_h = 0.01 y2(analytic)= = 0.33048244220531083551788851360545 y2(numeric) = = 0.33048244219304952284103873114013 absolute error = 1.226131267684978246532e-11 relative error = 3.7101252928990682136476147834340e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.63 y1(analytic)= = 0.9404601803291847022330517254913 y1(numeric) = = 0.94046018030014576322103451055104 absolute error = 2.903893901201721494026e-11 relative error = 3.0877372183746106477591027649310e-09 % glob_h = 0.01 y2(analytic)= = 0.3399038823185127893883579996919 y2(numeric) = = 0.33990388230594165791556202253367 absolute error = 1.257113147279597715823e-11 relative error = 3.6984371543647100253146124156520e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.64 y1(analytic)= = 0.93701417553920401790679870409782 y1(numeric) = = 0.93701417551024796473852826149497 absolute error = 2.895605316827044260285e-11 relative error = 3.0902470767432847215788187578028e-09 % glob_h = 0.01 y2(analytic)= = 0.34929133232673518306955111899986 y2(numeric) = = 0.34929133231385460051741503120022 absolute error = 1.288058255213608779964e-11 relative error = 3.6876330329569395837383399771406e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.65 y1(analytic)= = 0.93347447011251195664891862480071 y1(numeric) = = 0.93347447008364207880062391769606 absolute error = 2.886987784829470710465e-11 relative error = 3.0927335211229731977669990113190e-09 % glob_h = 0.01 y2(analytic)= = 0.35864385349280004325274828879219 y2(numeric) = = 0.35864385347961041217733880178775 absolute error = 1.318963107540948700444e-11 relative error = 3.6776403518300573689021105129450e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.66 y1(analytic)= = 0.92984141801670144297579140732785 y1(numeric) = = 0.92984141798792103014131359185153 absolute error = 2.878041283447781547632e-11 relative error = 3.0951958341310273951567013619707e-09 % glob_h = 0.01 y2(analytic)= = 0.36796051057238450511113950296911 y2(numeric) = = 0.36796051055888626295627709193713 absolute error = 1.349824215486241103198e-11 relative error = 3.6683942344424652655364893806010e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.67 y1(analytic)= = 0.92611538255395452461740229251973 y1(numeric) = = 0.92611538252526686633895539921672 absolute error = 2.868765827844689330301e-11 relative error = 3.0976332775441811640268894134085e-09 % glob_h = 0.01 y2(analytic)= = 0.37724037190754446521863585530426 y2(numeric) = = 0.37724037189373808436030083663647 absolute error = 1.380638085833501866779e-11 relative error = 3.6598365091525092877520971094241e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.68 y1(analytic)= = 0.92229673632471245706337804598795 y1(numeric) = = 0.92229673629612084236144535120848 absolute error = 2.859161470193269477947e-11 relative error = 3.1000450913301792486598513751589e-09 % glob_h = 0.01 y2(analytic)= = 0.38648250951987959958117999625914 y2(numeric) = = 0.3864825095057655873680182906472 absolute error = 1.411401221316170561194e-11 relative error = 3.6519148643221381173181308486087e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.69 y1(analytic)= = 0.91838586119041596993677070896915 y1(numeric) = = 0.9183858611619236869391779214391 absolute error = 2.849228299759278753005e-11 relative error = 3.1024304926320358949744953798948e-09 % glob_h = 0.01 y2(analytic)= = 0.39568599920333043035638964856538 y2(numeric) = = 0.39568599918890932914630540493165 absolute error = 1.442110121008424363373e-11 relative error = 3.6445821280306911006252540705545e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.7 y1(analytic)= = 0.91438314823531944113790184347665 y1(numeric) = = 0.91438314820692977670810840113572 absolute error = 2.838966442979344234093e-11 relative error = 3.1047886747019610408555425437645e-09 % glob_h = 0.01 y2(analytic)= = 0.40484992061659816163219284838685 y2(numeric) = = 0.40484992060187054882501553679487 absolute error = 1.472761280717731159198e-11 relative error = 3.6377956514717183298614783956095e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.71 y1(analytic)= = 0.91028899772738279730903147185009 y1(numeric) = = 0.91028899769909903667368140934859 absolute error = 2.828376063535006250150e-11 relative error = 3.1071188057817878706370278902004e-09 % glob_h = 0.01 y2(analytic)= = 0.41397335737517804235789332163191 y2(numeric) = = 0.41397335736014453042410733832376 absolute error = 1.503351193378598330815e-11 relative error = 3.6315167790282044041528885306156e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.72 y1(analytic)= = 0.90610381907824505139721526949621 y1(numeric) = = 0.90610381905007047777298927746954 absolute error = 2.817457362422599202667e-11 relative error = 3.1094200279265156399990399390715e-09 % glob_h = 0.01 y2(analytic)= = 0.4230553971429970531680671023396 y2(numeric) = = 0.42305539712765828967359236712491 absolute error = 1.533876349447473521469e-11 relative error = 3.6257103911358625685981538032871e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=9.76 NO POLE NO POLE x[1] = = 6.73 y1(analytic)= = 0.90182803080228347992823845092193 y1(numeric) = = 0.90182803077422137414804890428993 absolute error = 2.806210578018954663200e-11 relative error = 3.1116914557673440396435770050709e-09 % glob_h = 0.01 y2(analytic)= = 0.43209513172364675340697248794899 y2(numeric) = = 0.43209513170800342103398495326481 absolute error = 1.564333237298753468418e-11 relative error = 3.6203445085311616682037165737397e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.74 y1(analytic)= = 0.89746206047476253403978171712343 y1(numeric) = = 0.89746206044681617417835260116644 absolute error = 2.794635986142911595699e-11 relative error = 3.1139321752103183786600847446017e-09 % glob_h = 0.01 y2(analytic)= = 0.44109165715120216514479800955267 y2(numeric) = = 0.44109165713525498170857944157564 absolute error = 1.594718343621856797703e-11 relative error = 3.6153899484777650411338934101012e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.75 y1(analytic)= = 0.89300634468907666934784015651711 y1(numeric) = = 0.89300634466124933034671396633713 absolute error = 2.782733900112619017998e-11 relative error = 3.1161412420664267864343692679317e-09 % glob_h = 0.01 y2(analytic)= = 0.45004407378061761237302894340979 y2(numeric) = = 0.45004407376436733083483577858454 absolute error = 1.625028153819316482525e-11 relative error = 3.6108200251770603270728174026320e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.76 y1(analytic)= = 0.88846132901309137032777760118066 y1(numeric) = = 0.88846132898538632361979143234186 absolute error = 2.770504670798616883880e-11 relative error = 3.1183176806086895339971461279280e-09 % glob_h = 0.01 y2(analytic)= = 0.45895148637769047587034244196452 y2(numeric) = = 0.45895148636113788434628396716536 absolute error = 1.655259152405847479916e-11 relative error = 3.6066102878761898681578059044366e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.77 y1(analytic)= = 0.88382746794458673507119597456095 y1(numeric) = = 0.88382746791700724820446916019584 absolute error = 2.757948686672681436511e-11 relative error = 3.1204604820514543455021707451438e-09 % glob_h = 0.01 y2(analytic)= = 0.46781300420858386743851424067973 y2(numeric) = = 0.46781300419172978920443079189722 absolute error = 1.685407823408344878251e-11 relative error = 3.6027382912529549779095801479134e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.78 y1(analytic)= = 0.87910522486580807602301372144549 y1(numeric) = = 0.87910522483835741228448950388962 absolute error = 2.745066373852421755587e-11 relative error = 3.1225686029467578743677192735385e-09 % glob_h = 0.01 y2(analytic)= = 0.47662774112889927131551532987128 y2(numeric) = = 0.47662774111174456480784765276232 absolute error = 1.715470650766767710896e-11 relative error = 3.5991833935298272832573159243692e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.79 y1(analytic)= = 0.87429507199712808160080523921695 y1(numeric) = = 0.87429507196980949963938909227371 absolute error = 2.731858196141614694324e-11 relative error = 3.1246409634922297814323388746307e-09 % glob_h = 0.01 y2(analytic)= = 0.48539481567229024557588423562982 y2(numeric) = = 0.4853948156548358043885256014395 absolute error = 1.745444118735863419032e-11 relative error = 3.5959265784871580396012663694599e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.8 y1(analytic)= = 0.86939749034982517244162463984627 y1(numeric) = = 0.86939749032264192589096198106372 absolute error = 2.718324655066265878255e-11 relative error = 3.1266764457445992298105548327413e-09 % glob_h = 0.01 y2(analytic)= = 0.49411335113860832222207937762034 y2(numeric) = = 0.49411335112085507509920249982568 absolute error = 1.775324712287687779466e-11 relative error = 3.5929502981385236174557431697402e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.81 y1(analytic)= = 0.86441296967798277440133792162495 y1(numeric) = = 0.8644129696509381115022740724675 absolute error = 2.704466289906384915745e-11 relative error = 3.1286738917324109588078483298292e-09 % glob_h = 0.01 y2(analytic)= = 0.50278247568157229145025704041701 y2(numeric) = = 0.50278247566352120227510829090741 absolute error = 1.805108917514874950960e-11 relative error = 3.5902383333227117418217244533839e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.82 y1(analytic)= = 0.8593420084295143183390798118649 y1(numeric) = = 0.85934200840261148156184517736451 absolute error = 2.690283677723463450039e-11 relative error = 3.1306321014610659380327992950755e-09 % glob_h = 0.01 y2(analytic)= = 0.51140132239595210323510587393918 y2(numeric) = = 0.51140132237760417101475975258461 absolute error = 1.834793222034612135457e-11 relative error = 3.5877756698760055474276906931664e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.83 y1(analytic)= = 0.85418511369631886414604447074346 y1(numeric) = = 0.85418511366956108981220801909754 absolute error = 2.675777433383645164592e-11 relative error = 3.1325498308027660797297624328741e-09 % glob_h = 0.01 y2(analytic)= = 0.51996902940425866791623244868196 y2(numeric) = = 0.51996902938561492676229971669787 absolute error = 1.864374115393273198409e-11 relative error = 3.5855483883902327251286546586937e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.84 y1(analytic)= = 0.84894280116357233341467033570359 y1(numeric) = = 0.84894280113696285131890456233175 absolute error = 2.660948209576577337184e-11 relative error = 3.1344257892633593307531593857989e-09 % glob_h = 0.01 y2(analytic)= = 0.52848473994293088687828048687001 y2(numeric) = = 0.52848473992399240598356383241581 absolute error = 1.893848089471665445420e-11 relative error = 3.5835435658486091737597274728223e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.85 y1(analytic)= = 0.84361559505815942158269502267307 y1(numeric) = = 0.84361559503170145461439568243325 absolute error = 2.645796696829934023982e-11 relative error = 3.1362586376174459360064796181345e-09 % glob_h = 0.01 y2(analytic)= = 0.53694760244801129469353804377026 y2(numeric) = = 0.53694760242877917830462960766559 absolute error = 1.923211638890843610467e-11 relative error = 3.5817491876724677497122513462386e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.86 y1(analytic)= = 0.83820402809625134631789261531055 y1(numeric) = = 0.83820402806994811008269660088896 absolute error = 2.630323623519601442159e-11 relative error = 3.1380469854024134980716334448408e-09 % glob_h = 0.01 y2(analytic)= = 0.54535677064030174523421450890992 y2(numeric) = = 0.54535677062077713262003005916813 absolute error = 1.952461261418444974179e-11 relative error = 3.5801540689154112373906862845642e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=9.96 NO POLE NO POLE x[1] = = 6.87 y1(analytic)= = 0.83270864143003467432496980448714 y1(numeric) = = 0.8327086414038893767662146383988 absolute error = 2.614529755875516608834e-11 relative error = 3.1397893882613117999384980678578e-09 % glob_h = 0.01 y2(analytic)= = 0.55371140360999062625673903471704 y2(numeric) = = 0.55371140359017469167298404072656 absolute error = 1.981593458375499399048e-11 relative error = 3.5787477835136741754396868701085e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.88 y1(analytic)= = 0.82712998459359655364754769203734 y1(numeric) = = 0.82712998456761239466771618418736 absolute error = 2.598415897983150784998e-11 relative error = 3.1414843451236516948645366214889e-09 % glob_h = 0.01 y2(analytic)= = 0.56201066590074313980714440648556 y2(numeric) = = 0.56201066588063709245670772706588 absolute error = 2.010604735043667941968e-11 relative error = 3.5775206006477489237963223690713e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.89 y1(analytic)= = 0.82146861544797176289690357116892 y1(numeric) = = 0.8214686154221519339790972735135 absolute error = 2.581982891780629765542e-11 relative error = 3.1431302952123084412434639843953e-09 % glob_h = 0.01 y2(analytic)= = 0.57025372759324623948957081536545 y2(numeric) = = 0.57025372757285132347884217953275 absolute error = 2.039491601072863583270e-11 relative error = 3.5764634273949078535281352608651e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.9 y1(analytic)= = 0.81572510012535707265675583635806 y1(numeric) = = 0.81572510009970475648624100085179 absolute error = 2.565231617051483550627e-11 relative error = 3.1447256148637205760114129236168e-09 % glob_h = 0.01 y2(analytic)= = 0.57843976438819987017378323298886 y2(numeric) = = 0.57843976436751736446489115803492 absolute error = 2.068250570889207495394e-11 relative error = 3.5755677569586529261240166298950e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.91 y1(analytic)= = 0.80990001297249849758146366703568 y1(numeric) = = 0.80990001294701686766733348274373 absolute error = 2.548162991413018429195e-11 relative error = 3.1462686141474917387071855753052e-09 % glob_h = 0.01 y2(analytic)= = 0.58656795768874621108689077188692 y2(numeric) = = 0.58656795766777742944585803025158 absolute error = 2.096878164103274163534e-11 relative error = 3.5748256218522461178132976787765e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.92 y1(analytic)= = 0.80399393649325710041525453243594 y1(numeric) = = 0.80399393646794932071225148241092 absolute error = 2.530777970300305002502e-11 relative error = 3.1477575332703146766405592439854e-09 % glob_h = 0.01 y2(analytic)= = 0.59463749468232867943364966670118 y2(numeric) = = 0.59463749466107497037446388105047 absolute error = 2.125370905918578565071e-11 relative error = 3.5742295514917181377885499259899e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.93 y1(analytic)= = 0.7980074612903590913042159244115 y1(numeric) = = 0.79800746126522831583475816267133 absolute error = 2.513077546945776174017e-11 relative error = 3.1491905387478326732616164297724e-09 % glob_h = 0.01 y2(analytic)= = 0.60264756842197250871320345485614 y2(numeric) = = 0.60264756840043525543780086971251 absolute error = 2.153725327540258514363e-11 relative error = 3.5737725337211097029406112996828e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.94 y1(analytic)= = 0.79194118600633604734257869694061 y1(numeric) = = 0.79194118598138541981903440062194 absolute error = 2.495062752354429631867e-11 relative error = 3.1505657193266211795599692691099e-09 % glob_h = 0.01 y2(analytic)= = 0.61059737790697877374216227215981 y2(numeric) = = 0.61059737788515939407632322031502 absolute error = 2.181937966583905184479e-11 relative error = 3.5734479798508268365563091512817e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.95 y1(analytic)= = 0.78579571726366115828212106433534 y1(numeric) = = 0.78579571723889381172937476582399 absolute error = 2.476734655274629851135e-11 relative error = 3.1518810816368972832962273340429e-09 % glob_h = 0.01 y2(analytic)= = 0.61848612816302379304876375210548 y2(numeric) = = 0.61848612814092373937391880482726 absolute error = 2.210005367484494727822e-11 relative error = 3.5732496928402733866730291922003e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.96 y1(analytic)= = 0.77957166960408748473023602213012 y1(numeric) = = 0.77957166957950654110859097067338 absolute error = 2.458094362164505145674e-11 relative error = 3.1531345455548308657606776247150e-09 % glob_h = 0.01 y2(analytic)= = 0.62631303032165589876462539228221 y2(numeric) = = 0.62631303029927665794557165394934 absolute error = 2.237924081905373833287e-11 relative error = 3.5731718382995193860142417608199e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.97 y1(analytic)= = 0.77326966542719429496029110091148 y1(numeric) = = 0.77326966540280286478875174288478 absolute error = 2.439143017153935802670e-11 relative error = 3.1543239392514209274782829352732e-09 % glob_h = 0.01 y2(analytic)= = 0.63407730169918162440334630007633 y2(numeric) = = 0.63407730167652471771187378029063 absolute error = 2.265690669147251978570e-11 relative error = 3.5732089180226465210341957031532e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.98 y1(analytic)= = 0.76689033492814762564938820182662 y1(numeric) = = 0.76689033490394880762936690344787 absolute error = 2.419881802002129837875e-11 relative error = 3.1554469939027934111653867386356e-09 % glob_h = 0.01 y2(analytic)= = 0.64177816587493342197291872817706 y2(numeric) = = 0.64177816585200040500734719755039 absolute error = 2.293301696557153062667e-11 relative error = 3.5733557457984016830317268765392e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 6.99 y1(analytic)= = 0.76043431603468129043558371128891 y1(numeric) = = 0.7604343160106781710750758771373 absolute error = 2.400311936050783415161e-11 relative error = 3.1565013380344501384868047396840e-09 % glob_h = 0.01 y2(analytic)= = 0.64941485276891108171546103891648 y2(numeric) = = 0.64941485274570354431608824856309 absolute error = 2.320753739937279035339e-11 relative error = 3.5736074252725785894811318481202e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7 y1(analytic)= = 0.75390225434330463814119752171918 y1(numeric) = = 0.75390225431950029137946928691057 absolute error = 2.380434676172823480861e-11 relative error = 3.1574844914694264995268809243407e-09 % glob_h = 0.01 y2(analytic)= = 0.65698659871878909039699909159364 y2(numeric) = = 0.6569865986953086565574617108191 absolute error = 2.348043383953738077454e-11 relative error = 3.5739593296617218084722366987869e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=186.9MB, alloc=4.4MB, time=10.16 x[1] = = 7.01 y1(analytic)= = 0.74729480305474343983322860314033 y1(numeric) = = 0.74729480303114092666606129642982 absolute error = 2.360251316716730671051e-11 relative error = 3.1583938588474692321251762466924e-09 % glob_h = 0.01 y2(analytic)= = 0.66449264655628222747563965930974 y2(numeric) = = 0.66449264653253055525018876102334 absolute error = 2.375167222545089828640e-11 relative error = 3.5744070831398045216685296786304e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.02 y1(analytic)= = 0.74061262290862036057837200261576 y1(numeric) = = 0.74061262288522272868390759202986 absolute error = 2.339763189446441058590e-11 relative error = 3.1592267226791921116899409427753e-09 % glob_h = 0.01 y2(analytic)= = 0.67193224568286176265215684265362 y2(numeric) = = 0.67193224565884054405885024158665 absolute error = 2.402121859330660106697e-11 relative error = 3.5749465437388941030091848833174e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.03 y1(analytic)= = 0.73385638211738154779102901107035 y1(numeric) = = 0.73385638209419183115626075290837 absolute error = 2.318971663476825816198e-11 relative error = 3.1599802358956693588031034648150e-09 % glob_h = 0.01 y2(analytic)= = 0.67930465214481468324633304256555 y2(numeric) = = 0.67930465212052564416614726740053 absolute error = 2.428903908018577516502e-11 relative error = 3.5755737876218488358352220837464e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.04 y1(analytic)= = 0.72702675629947594346041470363747 y1(numeric) = = 0.72702675627649716200836721981635 absolute error = 2.297878145204748382112e-11 relative error = 3.1606514138500417417921894263521e-09 % glob_h = 0.01 y2(analytic)= = 0.68660912870763844553886600593178 y2(numeric) = = 0.68660912868308334561073116288136 absolute error = 2.455509992813484305042e-11 relative error = 3.5762850946000931695964486327236e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.05 y1(analytic)= = 0.72012442841179400226985642191336 y1(numeric) = = 0.72012442838902916148749942965486 absolute error = 2.276484078235699225850e-11 relative error = 3.1612371257233905939992743902870e-09 % glob_h = 0.01 y2(analytic)= = 0.69384494492976381066570317267167 y2(numeric) = = 0.6938449449049444431774644348375 absolute error = 2.481936748823873783417e-11 relative error = 3.5770769347827619271215533768320e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.06 y1(analytic)= = 0.71315008868137257168017038770663 y1(numeric) = = 0.71315008865882466224711029947381 absolute error = 2.254790943306008823282e-11 relative error = 3.1617340852823255048442631774500e-09 % glob_h = 0.01 y2(analytic)= = 0.70101137723559839284264938267611 y2(numeric) = = 0.70101137721051658461795931661201 absolute error = 2.508180822469006606410e-11 relative error = 3.5779459562552125162419662673580e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.07 y1(analytic)= = 0.70610443453637276343219570039922 y1(numeric) = = 0.70610443451404476085018930077467 absolute error = 2.232800258200639962455e-11 relative error = 3.1621388409303698183389360203483e-09 % glob_h = 0.01 y2(analytic)= = 0.70810770898788361562629490244864 y2(numeric) = = 0.70810770896254122690744132069462 absolute error = 2.534238871885358175402e-11 relative error = 3.5788889736952734825234149308485e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.08 y1(analytic)= = 0.69898817053633771862381721583248 y1(numeric) = = 0.69898817051423258284715160568773 absolute error = 2.210513577666561014475e-11 relative error = 3.1624477649892429437449274499639e-09 % glob_h = 0.01 y2(analytic)= = 0.71513323055935784057593494120609 y2(numeric) = = 0.71513323053375676490260944709551 absolute error = 2.560107567332549411058e-11 relative error = 3.5799029578447957495787642181368e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.09 y1(analytic)= = 0.69180200830173724052685126905588 y1(numeric) = = 0.69180200827985791559363424588559 absolute error = 2.187932493321702317029e-11 relative error = 3.1626570421394482399377905776744e-09 % glob_h = 0.01 y2(analytic)= = 0.72208723940371850206333353930838 y2(numeric) = = 0.72208723937786066614734640802423 absolute error = 2.585783591598713128415e-11 relative error = 3.5809850257622447997630915970120e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.1 y1(analytic)= = 0.68454666644280634062179994208932 y1(numeric) = = 0.68454666642115575428620495877002 absolute error = 2.165058633559498331930e-11 relative error = 3.1627626569420863610694928277717e-09 % glob_h = 0.01 y2(analytic)= = 0.72896904012587615207598576785319 y2(numeric) = = 0.72896904009976351567193328546729 absolute error = 2.611263640405248238590e-11 relative error = 3.5821324317893434704027538480345e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.11 y1(analytic)= = 0.67722287048768481393656938730488 y1(numeric) = = 0.67722287046626587730207919978322 absolute error = 2.141893663449018752166e-11 relative error = 3.1627603803554191023501820160210e-09 % glob_h = 0.01 y2(analytic)= = 0.73577794455149338966794275540197 y2(numeric) = = 0.73577794452512794543983361541664 absolute error = 2.636544422810913998533e-11 relative error = 3.5833425591712548864256848514343e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.12 y1(analytic)= = 0.66983135280986502967173484698978 y1(numeric) = = 0.6698313527886806368254279245057 absolute error = 2.118439284630692248408e-11 relative error = 3.1626457551502845302350502058079e-09 % glob_h = 0.01 y2(analytic)= = 0.74251327179580172122320337404692 y2(numeric) = = 0.74251327176918549460705120871823 absolute error = 2.661622661615216532869e-11 relative error = 3.5846129122755779099888645307313e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.13 y1(analytic)= = 0.66237285255495519227282986964329 y1(numeric) = = 0.66237285253400821992075359904693 absolute error = 2.094697235207627059636e-11 relative error = 3.1624140801178683358204481089261e-09 % glob_h = 0.01 y2(analytic)= = 0.74917434833168946990299343804552 y2(numeric) = = 0.74917434830482451896538303944485 absolute error = 2.686495093761039860067e-11 relative error = 3.5859411093605956652427077005334e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.14 y1(analytic)= = 0.6548481155667653965625220817479 y1(numeric) = = 0.65484811554605870366619675027318 absolute error = 2.070669289632533147472e-11 relative error = 3.1620603929514048229431837669911e-09 % glob_h = 0.01 y2(analytic)= = 0.75576050805705392554272742250943 y2(numeric) = = 0.75576050802994234083536268582086 absolute error = 2.711158470736473668857e-11 relative error = 3.5873248758478429286924360892402e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=190.7MB, alloc=4.4MB, time=10.35 x[1] = = 7.15 y1(analytic)= = 0.64725789431272386826556754869712 y1(numeric) = = 0.64725789429226029567966503720865 absolute error = 2.046357258590251148847e-11 relative error = 3.1615794516699240023356893994596e-09 % glob_h = 0.01 y2(analytic)= = 0.76227109236141099983978961046771 y2(numeric) = = 0.76227109233405490425003170936729 absolute error = 2.735609558975790110042e-11 relative error = 3.5887620380582030961765813950921e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.16 y1(analytic)= = 0.63960294780863084824033830372473 y1(numeric) = = 0.63960294778841321835157936495677 absolute error = 2.021762988875893876796e-11 relative error = 3.1609657144369591059314096276194e-09 % glob_h = 0.01 y2(analytic)= = 0.76870545019175572592212375115303 y2(numeric) = = 0.76870545016415727451952853221716 absolute error = 2.759845140259521893587e-11 relative error = 3.5902505173744648218450631863475e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.17 y1(analytic)= = 0.63188404154275764496579500462555 y1(numeric) = = 0.6318840415227887613331089382823 absolute error = 1.996888363268606634325e-11 relative error = 3.1602133176099263068261197800921e-09 % glob_h = 0.01 y2(analytic)= = 0.77506293811766701630255793723995 y2(numeric) = = 0.77506293808982839618142199712841 absolute error = 2.783862012113594011154e-11 relative error = 3.5917883247966102538434369028780e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.18 y1(analytic)= = 0.62410194739929844531540544224327 y1(numeric) = = 0.62410194737958109231139591102896 absolute error = 1.971735300400953121431e-11 relative error = 3.1593160518363887329336037274185e-09 % glob_h = 0.01 y2(analytic)= = 0.78134292039565016879732305266329 y2(numeric) = = 0.78134292036757359891524843826268 absolute error = 2.807656988207461440061e-11 relative error = 3.5933735558591131613933417614465e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.19 y1(analytic)= = 0.61625744358118253837314156381981 y1(numeric) = = 0.61625744356171948082690222151572 absolute error = 1.946305754623934230409e-11 relative error = 3.1582673359912740286637183892884e-09 % glob_h = 0.01 y2(analytic)= = 0.78754476903271068621179151537509 y2(numeric) = = 0.78754476900439841722427946311511 absolute error = 2.831226898751205225998e-11 relative error = 3.5950043858822331478166316305720e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.2 y1(analytic)= = 0.60835131453225467100485047909372 y1(numeric) = = 0.60835131451304865384617400369933 absolute error = 1.920601715867647539439e-11 relative error = 3.1570601887239245896446544919715e-09 % glob_h = 0.01 y2(analytic)= = 0.79366786384915305246444574764358 y2(numeric) = = 0.79366786382060736655553035375652 absolute error = 2.854568590891539388706e-11 relative error = 3.5966790655317341247503146886153e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.21 y1(analytic)= = 0.60038435085883131708459282452204 y1(numeric) = = 0.60038435083988506498961686623045 absolute error = 1.894625209497595829159e-11 relative error = 3.1556871973551489760642328448822e-09 % glob_h = 0.01 y2(analytic)= = 0.79971159254059818532379611604323 y2(numeric) = = 0.79971159251182139603272930457027 absolute error = 2.877678929106681147296e-11 relative error = 3.5983959166636599718953024028877e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.22 y1(analytic)= = 0.5923573492506407046836562940431 y1(numeric) = = 0.59235734923195692172198975943023 absolute error = 1.868378296166653461287e-11 relative error = 3.1541404838316566031971099550261e-09 % glob_h = 0.01 y2(analytic)= = 0.80567535073921336406465568768538 y2(numeric) = = 0.8056753507102078161086553174874 absolute error = 2.900554795600037019798e-11 relative error = 3.6001533284327931427201139315372e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.23 y1(analytic)= = 0.58427111240115450715364234396222 y1(numeric) = = 0.58427111238273587643701534423741 absolute error = 1.841863071662699972481e-11 relative error = 3.1524116674077424243707178219248e-09 % glob_h = 0.01 y2(analytic)= = 0.81155854207414850910203094484469 y2(numeric) = = 0.81155854204491657819510437069378 absolute error = 2.923193090692657415091e-11 relative error = 3.6019497536452252769188139407198e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.24 y1(analytic)= = 0.57612644892731916486812772715933 y1(numeric) = = 0.57612644890916834820060841965684 absolute error = 1.815081666751930750249e-11 relative error = 3.1504918236810737482220257016392e-09 % glob_h = 0.01 y2(analytic)= = 0.81736057823117277002502846739325 y2(numeric) = = 0.81736057820171686269288434334934 absolute error = 2.945590733214412404391e-11 relative error = 3.6037837053371024491190484845013e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.25 y1(analytic)= = 0.56792417328869486442383634821816 y1(numeric) = = 0.56792417327081450195365779650804 absolute error = 1.788036247017855171012e-11 relative error = 3.1483714395600070805796556264133e-09 % glob_h = 0.01 y2(analytic)= = 0.82308087901150545842167118341206 y2(numeric) = = 0.82308087898182801181273276907144 absolute error = 2.967744660893841434062e-11 relative error = 3.6056537535630890712471978626798e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.26 y1(analytic)= = 0.55966510570601026133601736290577 y1(numeric) = = 0.55966510568840297120905743197491 absolute error = 1.760729012695993093086e-11 relative error = 3.1460403636829498486394671140204e-09 % glob_h = 0.01 y2(analytic)= = 0.82871887238983544245036732029002 y2(numeric) = = 0.82871887235993892414290102207345 absolute error = 2.989651830746629821657e-11 relative error = 3.6075585223794392471849222529206e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.27 y1(analytic)= = 0.55135007207914109068788914600869 y1(numeric) = = 0.551350072061809468702846334913 absolute error = 1.733162198504281109569e-11 relative error = 3.1434877517445976869880811993508e-09 % glob_h = 0.01 y2(analytic)= = 0.83427399457152320126692424372665 y2(numeric) = = 0.83427399454141010907229759409935 absolute error = 3.011309219462664962730e-11 relative error = 3.6094966870077863906290630901412e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.28 y1(analytic)= = 0.5429799039045208678047332531733 y1(numeric) = = 0.54297990388746748707004124839751 absolute error = 1.705338073469200477579e-11 relative error = 3.1407020061078945190688219844560e-09 % glob_h = 0.01 y2(analytic)= = 0.83974569004897981914933270304968 y2(numeric) = = 0.83974569001865268091141645037806 absolute error = 3.032713823791625267162e-11 relative error = 3.6114669711668734710034155624131e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.29 y1(analytic)= = 0.53455543819199193781374678066391 y1(numeric) = = 0.53455543817521934840627038915198 absolute error = 1.677258940747639151193e-11 relative error = 3.1376707089924537846570481269235e-09 % glob_h = 0.01 y2(analytic)= = 0.84513341165721728146789134291882 y2(numeric) = = 0.84513341162667865485862079351425 absolute error = 3.053862660927054940457e-11 relative error = 3.6134681445604583130344969696635e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=10.55 NO POLE NO POLE x[1] = = 7.3 y1(analytic)= = 0.52607751738110518891540657673769 y1(numeric) = = 0.52607751736461591754096156818312 absolute error = 1.648927137444500855457e-11 relative error = 3.1343805484277560647315485875495e-09 % glob_h = 0.01 y2(analytic)= = 0.85043662062856451751736622796691 y2(numeric) = = 0.85043662059781698982847744968998 absolute error = 3.074752768888877827693e-11 relative error = 3.6154990205105507219118521749662e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.31 y1(analytic)= = 0.51754698925687679932526816177548 y1(numeric) = = 0.51754698924067334898100741529345 absolute error = 1.620345034426074648203e-11 relative error = 3.1308172360400696628082291906814e-09 % glob_h = 0.01 y2(analytic)= = 0.85565478664654371865249871479739 y2(numeric) = = 0.85565478661558990658345567834181 absolute error = 3.095381206904303645558e-11 relative error = 3.6175584537259795686378852028535e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.32 y1(analytic)= = 0.50896470686501044214130270040307 y1(numeric) = = 0.50896470684909529178001091115537 absolute error = 1.591515036129178924770e-11 relative error = 3.1269654156025529755673732256484e-09 % glob_h = 0.01 y2(analytic)= = 0.86078738789890154413994490267433 y2(numeric) = = 0.86078738786774409358207410226253 absolute error = 3.115745055787080041180e-11 relative error = 3.6196453381970561534676775332718e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.33 y1(analytic)= = 0.5003315284265934258456373647886 y1(numeric) = = 0.50033152841096903004197642150626 absolute error = 1.562439580366094328234e-11 relative error = 3.1228085611145510819938939251387e-09 % glob_h = 0.01 y2(analytic)= = 0.86583391112978991165025399319452 y2(numeric) = = 0.86583391109843149746710355284255 absolute error = 3.135841418315044035197e-11 relative error = 3.6217586052078021529564833903106e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.34 y1(analytic)= = 0.49164831725227530075556260245278 y1(numeric) = = 0.49164831723694408937430959710982 absolute error = 1.533121138125300534296e-11 relative error = 3.1183288629840325122722867608981e-09 % glob_h = 0.01 y2(analytic)= = 0.87079385169109115435432020823595 y2(numeric) = = 0.87079385165953448015826094292814 absolute error = 3.155667419605926530781e-11 relative error = 3.6238972214578525046822811476705e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.35 y1(analytic)= = 0.48291594165593751349164361829989 y1(numeric) = = 0.48291594164090189135796329444586 absolute error = 1.503562213368032385403e-11 relative error = 3.1135071006607468349383255662639e-09 % glob_h = 0.01 y2(analytic)= = 0.87566671359288241215136944266837 y2(numeric) = = 0.87566671356113021007645580566739 absolute error = 3.175220207491363700098e-11 relative error = 3.6260601872867313041890131766890e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.36 y1(analytic)= = 0.47413527486786274242554754491746 y1(numeric) = = 0.47413527485312508899734083138676 absolute error = 1.473765342820671353070e-11 relative error = 3.1083224998000761783660762338318e-09 % glob_h = 0.01 y2(analytic)= = 0.88045200955303421063141137233862 y2(numeric) = = 0.88045200952108924110252068038986 absolute error = 3.194496952889069194876e-11 relative error = 3.6282465349937372184695475646224e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.37 y1(analytic)= = 0.46530719494741259710168287249685 y1(numeric) = = 0.46530719493297526614405298439111 absolute error = 1.443733095762988810574e-11 relative error = 3.1027525717201826422581728049628e-09 % glob_h = 0.01 y2(analytic)= = 0.88514926104593826795559278348171 y2(numeric) = = 0.88514926101380331945386157079703 absolute error = 3.213494850173121268468e-11 relative error = 3.6304553272471685866821395708095e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.38 y1(analytic)= = 0.45643258469522241378994063317773 y1(numeric) = = 0.45643258468108773305181805217615 absolute error = 1.413468073812258100158e-11 relative error = 3.0967729325374196927184806273565e-09 % glob_h = 0.01 y2(analytic)= = 0.88975799835035965691437045860369 y2(numeric) = = 0.88975799831803754573894726817397 absolute error = 3.232211117542319042972e-11 relative error = 3.6326856555770713544136777177103e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.39 y1(analytic)= = 0.44751233156492192761681130589502 y1(numeric) = = 0.44751233155109219850977877709886 absolute error = 1.382972910703252879616e-11 relative error = 3.0903570989140909064093587173912e-09 % glob_h = 0.01 y2(analytic)= = 0.89427776059640853698717447034021 y2(numeric) = = 0.89427776056390210701330884727493 absolute error = 3.250642997386562306528e-11 relative error = 3.6349366389461089400826359954171e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.4 y1(analytic)= = 0.43854732757439064913409846870034 y1(numeric) = = 0.43854732756086814641345697137551 absolute error = 1.352250272064149732483e-11 relative error = 3.0834762568123686311807424752505e-09 % glob_h = 0.01 y2(analytic)= = 0.89870809581162675926949889653456 y2(numeric) = = 0.89870809577893888170298680270424 absolute error = 3.268787756651209383032e-11 relative error = 3.6372074223935353670134321875855e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.41 y1(analytic)= = 0.42953846921655681971361872084562 y1(numeric) = = 0.42953846920334379116173518560547 absolute error = 1.321302855188353524015e-11 relative error = 3.0760989989983954328143341827339e-09 % glob_h = 0.01 y2(analytic)= = 0.90304856096618473564533262355124 y2(numeric) = = 0.90304856093331830877333894576223 absolute error = 3.286642687199367778901e-11 relative error = 3.6394971757476044945682279408078e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.42 y1(analytic)= = 0.42048665736974886579801444857924 y1(numeric) = = 0.42048665735684753190999180376246 absolute error = 1.290133388802264481678e-11 relative error = 3.0681910262560467636150954959146e-09 % glob_h = 0.01 y2(analytic)= = 0.907298722017184052555676926842 y2(numeric) = = 0.90729872198414200149395620204706 absolute error = 3.304205106172072479494e-11 relative error = 3.6418050924020716402911795726325e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.43 y1(analytic)= = 0.41139279720760831678754748094372 y1(numeric) = = 0.41139279719502087045925741620514 absolute error = 1.258744632829006473858e-11 relative error = 3.0597148063187509650739637641130e-09 % glob_h = 0.01 y2(analytic)= = 0.91145815395206139913869169875056 y2(numeric) = = 0.9114581539188466755752286293405 absolute error = 3.321472356346306941006e-11 relative error = 3.6441303881527417364793455774599e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=10.75 NO POLE NO POLE x[1] = = 7.44 y1(analytic)= = 0.40225779810857319519601263802318 y1(numeric) = = 0.40225779809630180141453127348386 absolute error = 1.227139378148136453932e-11 relative error = 3.0506291833699141766179649725671e-09 % glob_h = 0.01 y2(analytic)= = 0.91552644083108946938482612848397 y2(numeric) = = 0.91552644079770505131991790845987 absolute error = 3.338441806490822002410e-11 relative error = 3.6464723000902926117584241951235e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.45 y1(analytic)= = 0.39308257356494093066132532351689 y1(numeric) = = 0.3930825735529877261978117682305 absolute error = 1.195320446351355528639e-11 relative error = 3.0408889295467008829800385722672e-09 % glob_h = 0.01 y2(analytic)= = 0.91950317582897058825213562158732 y2(numeric) = = 0.91950317579541947973493854032695 absolute error = 3.355110851719708126037e-11 relative error = 3.6488300855458550250138747125760e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.46 y1(analytic)= = 0.38386804109151989144360145049109 y1(numeric) = = 0.38386804107988698454865902449307 absolute error = 1.163290689494242599802e-11 relative error = 3.0304442281427035313327664730773e-09 % glob_h = 0.01 y2(analytic)= = 0.92338796127551890241383466678817 y2(numeric) = = 0.92338796124180413327539790114031 absolute error = 3.371476913843676564786e-11 relative error = 3.6512030210860645127322493566101e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.47 y1(analytic)= = 0.37461512213387866818145642231011 y1(numeric) = = 0.37461512212256813828301610214204 absolute error = 1.131052989844032016807e-11 relative error = 3.0192400760581687797009250762644e-09 % glob_h = 0.01 y2(analytic)= = 0.92718040869542706745291260754133 y2(numeric) = = 0.92718040866155169303572255505354 absolute error = 3.387537441719005248779e-11 relative error = 3.6535904015545155804800330008752e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.48 y1(analytic)= = 0.36532474197620228490168886350835 y1(numeric) = = 0.36532474196521618230545429187021 absolute error = 1.098610259623457163814e-11 relative error = 3.0072155903829312050075505700277e-09 % glob_h = 0.01 y2(analytic)= = 0.93088013884711345486823165222931 y2(numeric) = = 0.93088013881308055575229059838634 absolute error = 3.403289911594105384297e-11 relative error = 3.6559915391567477622912860786597e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.49 y1(analytic)= = 0.35599782964876455158446189735926 y1(numeric) = = 0.35599782963810489717695507345563 absolute error = 1.065965440750682390363e-11 relative error = 2.9943032006750934907221132089353e-09 % glob_h = 0.01 y2(analytic)= = 0.9344867817606459942037790778139 y2(numeric) = = 0.93448678172645867592924242818109 absolute error = 3.418731827453664963281e-11 relative error = 3.6584057625860769396992454011751e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.5 y1(analytic)= = 0.3466353178350258109716193361719 y1(numeric) = = 0.34663531782469459592586587440387 absolute error = 1.033121504575346176803e-11 relative error = 2.9804277043317317720142001017743e-09 % glob_h = 0.01 y2(analytic)= = 0.93799997677473885794846379814905 y2(numeric) = = 0.93799997674040025073486054222542 absolute error = 3.433860721360325592363e-11 relative error = 3.6608324161877552831674946190814e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.51 y1(analytic)= = 0.33723814277836536976603766643119 y1(numeric) = = 0.33723814276836455524993027736322 absolute error = 1.000081451610738906797e-11 relative error = 2.9655051571909454671855536363708e-09 % glob_h = 0.01 y2(analytic)= = 0.94141937257281828956879778527965 y2(numeric) = = 0.94141937253833154803085929261596 absolute error = 3.448674153793849266369e-11 relative error = 3.6632708591591003701995881550585e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.52 y1(analytic)= = 0.32780724418845794090117117865875 y1(numeric) = = 0.32780724417878945778854978767986 absolute error = 9.66848311262139097889e-12 relative error = 2.9494415648309877306208153007079e-09 % glob_h = 0.01 y2(analytic)= = 0.94474462721815396812171383209535 y2(numeric) = = 0.94474462718352227098183651277072 absolute error = 3.463169713987731932463e-11 relative error = 3.6657204647833794635018682402395e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.53 y1(analytic)= = 0.31834356514730345915854391610429 y1(numeric) = = 0.3183435651379692077430305919263 absolute error = 9.33425141551332417799e-12 relative error = 2.9321313315047512581609836558482e-09 % glob_h = 0.01 y2(analytic)= = 0.94797540818805239634033441415349 y2(numeric) = = 0.94797540815327894613770220497769 absolute error = 3.477345020263220917580e-11 relative error = 3.6681806196953695257009376643802e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.54 y1(analytic)= = 0.30884805201491966707331846711522 y1(numeric) = = 0.30884805200592151678494508422871 absolute error = 8.99815028837338288651e-12 relative error = 2.9134554126761029525966214616875e-09 % glob_h = 0.01 y2(analytic)= = 0.95111139240710889288237746887495 y2(numeric) = = 0.95111139237219691567877053364021 absolute error = 3.491197720360693523474e-11 relative error = 3.6706507231766381486088441560737e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.55 y1(analytic)= = 0.29932165433470690179076179452426 y1(numeric) = = 0.29932165432604669091542810098806 absolute error = 8.66021087533369353620e-12 relative error = 2.8932791029043587640703315210654e-09 % glob_h = 0.01 y2(analytic)= = 0.95415226627951486356968415270904 y2(numeric) = = 0.9541522662444676086520006094028 absolute error = 3.504725491768354330624e-11 relative error = 3.6731301864787059549641272816584e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.56 y1(analytic)= = 0.28976532473849454631606004072774 y1(numeric) = = 0.28976532473017408171785954522205 absolute error = 8.32046459820049550569e-12 relative error = 2.8714493722495927398821592791240e-09 % glob_h = 0.01 y2(analytic)= = 0.95709772572041712091866725978209 y2(numeric) = = 0.95709772568523786049818516983948 absolute error = 3.517926042048208994261e-11 relative error = 3.6756184321723578914157425995017e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.57 y1(analytic)= = 0.28018001885127864043322963344168 y1(numeric) = = 0.28018001884329969727968046339193 absolute error = 7.97894315354917004975e-12 relative error = 2.8477916399114972200266729867038e-09 % glob_h = 0.01 y2(analytic)= = 0.9599474761863261160558599363545 y2(numeric) = = 0.95994747615101814496426721072385 absolute error = 3.530797109159272563065e-11 relative error = 3.6781148935214698148213389363987e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=202.1MB, alloc=4.4MB, time=10.96 x[1] = = 7.58 y1(analytic)= = 0.27056669519566017745264774140798 y1(numeric) = = 0.27056669518802449894286535721017 absolute error = 7.63567850978238419781e-12 relative error = 2.8221058413196963879025630115676e-09 % glob_h = 0.01 y2(analytic)= = 0.96270123270457004222071324501035 y2(numeric) = = 0.96270123266913667760293353897668 absolute error = 3.543336461777970603367e-11 relative error = 3.6806190138798084651867812303072e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.59 y1(analytic)= = 0.26092631509599364287789283974354 y1(numeric) = = 0.26092631508870293997374121871582 absolute error = 7.29070290415162102772e-12 relative error = 2.7941616013200521835896916736127e-09 % glob_h = 0.01 y2(analytic)= = 0.96535871990179186446983730325883 y2(numeric) = = 0.96535871986623644547368038656651 absolute error = 3.555541899615691669232e-11 relative error = 3.6831302461093478532178673669173e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.6 y1(analytic)= = 0.2512598425822553800581527493518 y1(numeric) = = 0.25125984257531133121841037702671 absolute error = 6.94404883974237232509e-12 relative error = 2.7636922670876412521667813741700e-09 % glob_h = 0.01 y2(analytic)= = 0.96791967203148642590346301802882 y2(numeric) = = 0.96791967199581231336612851881581 absolute error = 3.567411253733449921301e-11 relative error = 3.6856480520187237572797979493404e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.61 y1(analytic)= = 0.24156824429364139590952548133473 y1(numeric) = = 0.24156824428704564682710220711744 absolute error = 6.59574908242327421729e-12 relative error = 2.7303874736141751835686271998288e-09 % glob_h = 0.01 y2(analytic)= = 0.97038383300057487672644928191342 y2(numeric) = = 0.97038383296478545285791311226422 absolute error = 3.578942386853616964920e-11 relative error = 3.6881719018205208708691452370817e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.62 y1(analytic)= = 0.23185248938190424684430586220556 y1(numeric) = = 0.23185248937565841018654639128086 absolute error = 6.24583665775947092470e-12 relative error = 2.6938838027619424335363756679462e-09 % glob_h = 0.01 y2(analytic)= = 0.97275095639501376872307481417792 y2(numeric) = = 0.97275095635911243678638799167057 absolute error = 3.590133193668682250735e-11 relative error = 3.6907012736061545761326199049168e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.63 y1(analytic)= = 0.22211354941443867113911268468874 y1(numeric) = = 0.22211354940854432629122218839081 absolute error = 5.89434484789049629793e-12 relative error = 2.6537529400749514284552888469085e-09 % glob_h = 0.01 y2(analytic)= = 0.97502080550443625425750800827313 y2(numeric) = = 0.97502080546842643824603799168709 absolute error = 3.600981601147001658604e-11 relative error = 3.6932356528371717153220488160996e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.64 y1(analytic)= = 0.21235239827712565909785786757179 y1(numeric) = = 0.21235239827158435190948490026235 absolute error = 5.54130718837296730944e-12 relative error = 2.6094865107863818977704905548172e-09 % glob_h = 0.01 y2(analytic)= = 0.97719315334582292570058900292222 y2(numeric) = = 0.97719315330970807001223406123865 absolute error = 3.611485568835494168357e-11 relative error = 3.6957745318518524321079312054540e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.65 y1(analytic)= = 0.20257001207694467652157832270579 y1(numeric) = = 0.20257001207175791905658993456608 absolute error = 5.18675746498838813971e-12 relative error = 2.5604764554282782061885531074413e-09 % glob_h = 0.01 y2(analytic)= = 0.97926778268619992821870693234383 y2(numeric) = = 0.97926778264998349732711446425861 absolute error = 3.621643089159246808522e-11 relative error = 3.6983174093860484707249353371900e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.66 y1(analytic)= = 0.19276736904436378018162733604724 y1(numeric) = = 0.19276736903953305047111096810542 absolute error = 4.83072971051636794182e-12 relative error = 2.5059893354692288930173693736333e-09 % glob_h = 0.01 y2(analytic)= = 0.98124448606436207613240849882713 y2(numeric) = = 0.98124448602804755425522861515978 absolute error = 3.631452187717988366735e-11 relative error = 3.7008637901072425386555943293880e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.67 y1(analytic)= = 0.18294544943551738620333684430217 y1(numeric) = = 0.18294544943104412800186328451877 absolute error = 4.47325820147355978340e-12 relative error = 2.4451322595210245855962466871037e-09 % glob_h = 0.01 y2(analytic)= = 0.98312306581161880055120454342521 y2(numeric) = = 0.98312306577520969131541061699522 absolute error = 3.640910923579392642999e-11 relative error = 3.7034131841608587186639209471687e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.68 y1(analytic)= = 0.17310523543418147350179398632598 y1(numeric) = = 0.1731052354300670960469753536754 absolute error = 4.11437745481863265058e-12 relative error = 2.3768070587229651031189092801030e-09 % glob_h = 0.01 y2(analytic)= = 0.98490333407156085370709936617771 y2(numeric) = = 0.98490333403506067981140764288474 absolute error = 3.650017389569172329297e-11 relative error = 3.7059651067278956966662376705972e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.69 y1(analytic)= = 0.16324771105355602466770129344408 y1(numeric) = = 0.16324771104980190244307770068956 absolute error = 3.75412222462359275452e-12 relative error = 2.2996476951471576024957336363111e-09 % glob_h = 0.01 y2(analytic)= = 0.98658511281884579333288164163472 y2(numeric) = = 0.986585112782258096207302392572 absolute error = 3.658769712557924906272e-11 relative error = 3.7085190775929929703725746282587e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.7 y1(analytic)= = 0.15337386203786452597738423957205 y1(numeric) = = 0.15337386203447199847867246486511 absolute error = 3.39252749871177470694e-12 relative error = 2.2119332809616782389999789043624e-09 % glob_h = 0.01 y2(analytic)= = 0.98816823387700036855239361872366 y2(numeric) = = 0.98816823384032870801494669612678 absolute error = 3.667166053744692259688e-11 relative error = 3.7110746207220754176878154044746e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.71 y1(analytic)= = 0.14348467576378036649494500705627 y1(numeric) = = 0.14348467576075073799968217963032 absolute error = 3.02962849526282742595e-12 relative error = 2.1114648509576883028751495026196e-09 % glob_h = 0.01 y2(analytic)= = 0.98965253893523802705902485016358 y2(numeric) = = 0.98965253889848598096965288980132 absolute error = 3.675204608937196036226e-11 relative error = 3.7136312638487538136333042254244e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.72 y1(analytic)= = 0.13358114114168999354450785925844 y1(numeric) = = 0.13358114113902453288512283536169 absolute error = 2.66546065938502389675e-12 relative error = 1.9953869510350718254760636697471e-09 % glob_h = 0.01 y2(analytic)= = 0.99103787956428986184572714465391 y2(numeric) = = 0.99103787952746102575744003385709 absolute error = 3.682883608828711079682e-11 relative error = 3.7161885380686882533806209598484e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.4MB, time=11.15 NO POLE NO POLE x[1] = = 7.73 y1(analytic)= = 0.12366424851680269815472846584235 y1(numeric) = = 0.12366424851450263849507323769851 absolute error = 2.30005965965522814384e-12 relative error = 1.8599228857503718347802435719750e-09 % glob_h = 0.01 y2(analytic)= = 0.99232411723124741440507015197626 y2(numeric) = = 0.99232411719434540121235475582634 absolute error = 3.690201319271539614992e-11 relative error = 3.7187459774411481151974049653440e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.74 y1(analytic)= = 0.11373498957011691941461449239512 y1(numeric) = = 0.11373498956818345802998763542496 absolute error = 1.93346138462685697016e-12 relative error = 1.6999706000191699621798621074390e-09 % glob_h = 0.01 y2(analytic)= = 0.99351112331341585013138653688732 y2(numeric) = = 0.99351112327644428971591604510276 absolute error = 3.697156041547049178456e-11 relative error = 3.7213031185970263142633512929300e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.75 y1(analytic)= = 0.10379435721925297102769406771382 y1(numeric) = = 0.10379435721768726908838788952838 absolute error = 1.56570193930617818544e-12 relative error = 1.5084653744700427548198986702542e-09 % glob_h = 0.01 y2(analytic)= = 0.99459877911117612061901080163979 y2(numeric) = = 0.9945987790741386594926884253575 absolute error = 3.703746112632237628229e-11 relative error = 3.7238595003525872770547121896964e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.76 y1(analytic)= = 0.093843345519162106709237592836475 y1(numeric) = = 0.093843345517965289067640301658057 absolute error = 1.196817641597291178418e-12 relative error = 1.2753356511068864228118853433942e-09 % glob_h = 0.01 y2(analytic)= = 0.99558697585985482665110036610261 y2(numeric) = = 0.9955869758227551275964724770086 absolute error = 3.709969905462788909401e-11 relative error = 3.7264146633282474140792885396464e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.77 y1(analytic)= = 0.083882949562721853437250999942011 y1(numeric) = = 0.083882949561895008418534860154986 absolute error = 8.26845018716139787025e-13 relative error = 9.8571285705431997656597658159561e-10 % glob_h = 0.01 y2(analytic)= = 0.9964756147406005949026315428916 y2(numeric) = = 0.99647561470344233661070570696222 absolute error = 3.715825829192583592938e-11 relative error = 3.7289681495717039825043133576610e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.78 y1(analytic)= = 0.073914165381227552941078415626023 y1(numeric) = = 0.073914165380771732137504504141074 absolute error = 4.55820803573911484949e-13 relative error = 6.1668937371195585622762371802519e-10 % glob_h = 0.01 y2(analytic)= = 0.99726460689026588072896372495315 y2(numeric) = = 0.99726460685305275743446743938171 absolute error = 3.721312329449628557144e-11 relative error = 3.7315195021847431944999713760287e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.79 y1(analytic)= = 0.063937989844790062190541929271678 y1(numeric) = = 0.063937989844706280259411748339076 absolute error = 8.3781931130180932602e-14 relative error = 1.3103622953045940756674518202294e-10 % glob_h = 0.01 y2(analytic)= = 0.99795387341029320886792773739019 y2(numeric) = = 0.99795387337302892998204403204656 absolute error = 3.726427888588370534363e-11 relative error = 3.7340682649530713167576523644931e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.8 y1(analytic)= = 0.053955420562649573032567912952475 y1(numeric) = = 0.053955420562938807497851753017717 absolute error = 2.89234465283840065242e-13 relative error = 5.3606192346883768424824382964209e-10 % glob_h = 0.01 y2(analytic)= = 0.99854334537460496343877332059609 y2(numeric) = = 0.99854334533729325317938973455545 absolute error = 3.731171025938358604064e-11 relative error = 3.7366139819785233859428766765811e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.81 y1(analytic)= = 0.043967455783415519510264690170958 y1(numeric) = = 0.043967455784078710567936270365672 absolute error = 6.63191057671580194714e-13 relative error = 1.5083680550870883016235797521588e-09 % glob_h = 0.01 y2(analytic)= = 0.99903296383649593826555065303152 y2(numeric) = = 0.99903296379914053528505844226699 absolute error = 3.735540298049221076453e-11 relative error = 3.7391561973130130890988455467456e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.82 y1(analytic)= = 0.03397509429524254879058651220993 y1(numeric) = = 0.033975094296280599117693056148722 absolute error = 1.038050327106543938792e-12 relative error = 3.0553272879419193953605396196787e-09 % glob_h = 0.01 y2(analytic)= = 0.99942267983452795827563734828205 y2(numeric) = = 0.99942267979713261528631812250118 absolute error = 3.739534298931922578087e-11 relative error = 3.7416944545935943729006906301724e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.83 y1(analytic)= = 0.023979335325952538020304662093397 y1(numeric) = = 0.023979335327366312587801192840233 absolute error = 1.413774567496530746836e-12 relative error = 5.8958038172410059238128854358187e-09 % glob_h = 0.01 y2(analytic)= = 0.99971245439742598251618324182164 y2(numeric) = = 0.9997124543599944659132205665943 absolute error = 3.743151660296267522734e-11 relative error = 3.7442282966780104883657340569205e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.84 y1(analytic)= = 0.013981178443112644825368713865179 y1(numeric) = = 0.013981178444902970714744974278335 absolute error = 1.790325889376260413156e-12 relative error = 1.2805257415609368553584468005248e-08 % glob_h = 0.01 y2(analytic)= = 0.99990225854797519918225139525021 y2(numeric) = = 0.9999022585105112886644052299817 absolute error = 3.746391051784616526851e-11 relative error = 3.7467572652801094765820445617666e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.85 y1(analytic)= = 0.0039816234540793835653399973691918 y1(numeric) = = 0.00398162345624704978906802056969 absolute error = 2.1676662237280232004982e-12 relative error = 5.4441768507947044648447656722524e-08 % glob_h = 0.01 y2(analytic)= = 0.99999207330591872295040007226969 y2(numeric) = = 0.99999207326842621113838224517514 absolute error = 3.749251181201782709455e-11 relative error = 3.7492809006045065762833736801521e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.86 y1(analytic)= = -0.00601832969398127714802450028153 y1(numeric) = = -0.0060183296914355198221945308083911 absolute error = 2.5457573258299694731389e-12 relative error = 4.2300064225060536398544791925083e-08 % glob_h = 0.01 y2(analytic)= = 0.99998188968985560485038706792968 y2(numeric) = = 0.99998188965233829690297631592117 absolute error = 3.751730794741075200851e-11 relative error = 3.7517987409798736976079459251975e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=11.35 NO POLE NO POLE x[1] = = 7.87 y1(analytic)= = -0.016017681014087797761105962616945 y1(numeric) = = -0.016017681011163236981974312745048 absolute error = 2.924560779131649871897e-12 relative error = 1.8258328259624183501483685479996e-08 % glob_h = 0.01 y2(analytic)= = 0.99987170871813896487559089033093 y2(numeric) = = 0.99987170868060067810352631459437 absolute error = 3.753828677206457573656e-11 relative error = 3.7543103224902339619365623300639e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.88 y1(analytic)= = -0.026015430579440932612672226052109 y1(numeric) = = -0.026015430576136894613515812681775 absolute error = 3.304037999156413370334e-12 relative error = 1.2700301035061387062052923855894e-08 % glob_h = 0.01 y2(analytic)= = 0.99966154140877415751963619401532 y2(numeric) = = 0.999661541371218720997328300989 absolute error = 3.755543652230789302632e-11 relative error = 3.7568151786036353508585336097158e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.89 y1(analytic)= = -0.03601057862341557658888876786824 y1(numeric) = = -0.036010578619731426351458500970096 absolute error = 3.684150237430266898144e-12 relative error = 1.0230744348647258668521065740547e-08 % glob_h = 0.01 y2(analytic)= = 0.99935140877831698042258494072934 y2(numeric) = = 0.99935140874074823459768375315758 absolute error = 3.756874582490118757176e-11 relative error = 3.7593128397975717258817342551735e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.9 y1(analytic)= = -0.046002125639536594497752959958488 y1(numeric) = = -0.046002125635471735912316163353809 absolute error = 4.064858585436796604679e-12 relative error = 8.8362407800200604613743881983206e-09 % glob_h = 0.01 y2(analytic)= = 0.9989413418397720363049105120439 y2(numeric) = = 0.9989413418021938326057705457269 absolute error = 3.757820369913996631700e-11 relative error = 3.7618028331805118538010531460606e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.91 y1(analytic)= = -0.055989072481428635663327058348253 y1(numeric) = = -0.055989072476982511684729311085008 absolute error = 4.446123978597747263245e-12 relative error = 7.9410566768587027957752337727942e-09 % glob_h = 0.01 y2(analytic)= = 0.99843138159949145835131001720205 y2(numeric) = = 0.99843138156190765879239222595601 absolute error = 3.758379955891779124604e-11 relative error = 3.7642846821088875719913350342538e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.92 y1(analytic)= = -0.065970420462729938841601739715093 y1(numeric) = = -0.065970420457902031641322886929494 absolute error = 4.827907200278852785599e-12 relative error = 7.3182907830735810395508190088076e-09 % glob_h = 0.01 y2(analytic)= = 0.997821579053074309169232028065 y2(numeric) = = 0.99782157901548878595448312220416 absolute error = 3.758552321474890586084e-11 relative error = 3.7667579057988808161724283856965e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.93 y1(analytic)= = -0.075945171456960136160759825113247 y1(numeric) = = -0.075945171451749967274939317786776 absolute error = 5.210168885820507326471e-12 relative error = 6.8604346871127008707647847980606e-09 % glob_h = 0.01 y2(analytic)= = 0.99711199518026706337880673223894 y2(numeric) = = 0.9971119951426836985030565745539 absolute error = 3.758336487575015768504e-11 relative error = 3.7692220189323358645668792118885e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.94 y1(analytic)= = -0.085912327997332069388669057070581 y1(numeric) = = -0.085912327991739199862076194060126 absolute error = 5.592869526592863010455e-12 relative error = 6.5099731982196368584026051473834e-09 % glob_h = 0.01 y2(analytic)= = 0.99630270093886568378166992769087 y2(numeric) = = 0.9963027009012883686300880053855 absolute error = 3.757731515158192230537e-11 relative error = 3.7716765312561077722824171880636e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.95 y1(analytic)= = -0.095870893376497637429153417081914 y1(numeric) = = -0.095870893370521667955078480173439 absolute error = 5.975969474074936908475e-12 relative error = 6.2333511909673324330263579718285e-09 % glob_h = 0.01 y2(analytic)= = 0.99539377725761990089598239019999 y2(numeric) = = 0.99539377722005253584163465152378 absolute error = 3.756736505434773867621e-11 relative error = 3.7741209471741405142826673819678e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.96 y1(analytic)= = -0.10581987174621770054541461887591 y1(numeric) = = -0.10581987173985827160145731234694 absolute error = 6.35942894395730652897e-12 relative error = 6.0096736454271977347046390566307e-09 % glob_h = 0.01 y2(analytic)= = 0.99438531502814040542377803103084 y2(numeric) = = 0.99438531499058689942332566136533 absolute error = 3.755350600045236966551e-11 relative error = 3.7765547653315487511493161142802e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.97 y1(analytic)= = -0.1157582682169460744032394119654 y1(numeric) = = -0.11575826821020286638297144219524 absolute error = 6.74320802026796977016e-12 relative error = 5.8252495688950006631497533911733e-09 % glob_h = 0.01 y2(analytic)= = 0.99327741509580976292465012621496 y2(numeric) = = 0.99327741505827403311223212010474 absolute error = 3.753572981241800611022e-11 relative error = 3.7789774781899552953582742945879e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.98 y1(analytic)= = -0.12568508895731765561757475983164 y1(numeric) = = -0.12568508895019038895805381782702 absolute error = 7.12726665952094200462e-12 relative error = 5.6707336714710398775207263952622e-09 % glob_h = 0.01 y2(analytic)= = 0.99207018824969795959673403629384 y2(numeric) = = 0.99207018821218393087607569931567 absolute error = 3.751402872065833697817e-11 relative error = 3.7813885715933121931971019999913e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 7.99 y1(analytic)= = -0.13559934129353073007282273015827 y1(numeric) = = -0.13559934128601916537793557042131 absolute error = 7.51156469488715973696e-12 relative error = 5.5395288968454058515333765906298e-09 % glob_h = 0.01 y2(analytic)= = 0.99076375521148358760200463441425 y2(numeric) = = 0.99076375517399519223679442181556 absolute error = 3.748839536521021259869e-11 relative error = 3.7837875243234067434182415853115e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8 y1(analytic)= = -0.14550003380861352586884138183119 y1(numeric) = = -0.14550003380071746402845412474244 absolute error = 7.89606184038725708875e-12 relative error = 5.4268453647052103704728467711807e-09 % glob_h = 0.01 y2(analytic)= = 0.98935824662338177780812359824529 y2(numeric) = = 0.98935824658592295501070096591853 absolute error = 3.745882279742263232676e-11 relative error = 3.7861738076442246314245514101268e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=213.6MB, alloc=4.4MB, time=11.56 x[1] = = 8.01 y1(analytic)= = -0.15538617644156508432007890033088 y1(numeric) = = -0.15538617643328436662497312210667 absolute error = 8.28071769510577822421e-12 relative error = 5.3291212157600426657773943672569e-09 % glob_h = 0.01 y2(analytic)= = 0.98785380303508008714350235847298 y2(numeric) = = 0.98785380299765478266189956602865 absolute error = 3.742530448160279244433e-11 relative error = 3.7885468848343105377160429806967e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.02 y1(analytic)= = -0.16525678058636053500335818521195 y1(numeric) = = -0.16525678057769504325593179947787 absolute error = 8.66549174742638573408e-12 relative error = 5.2436527667304635352091819985777e-09 % glob_h = 0.01 y2(analytic)= = 0.98625057488968364696595847332931 y2(numeric) = = 0.98625057485229581266933953875182 absolute error = 3.738783429661893457749e-11 relative error = 3.7909062107062319386817181797084e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.03 y1(analytic)= = -0.17511085919081087440931123207029 y1(numeric) = = -0.17511085918176053103002361012465 absolute error = 9.05034337928762194564e-12 relative error = 5.1683507357050008613693213170096e-09 % glob_h = 0.01 y2(analytic)= = 0.98454872250867097791841622619989 y2(numeric) = = 0.98454872247132457138095648678179 absolute error = 3.734640653745973941810e-11 relative error = 3.7932512311122141993800828130697e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.04 y1(analytic)= = -0.18494742685526736230198103982575 y1(numeric) = = -0.18494742684583213043152226270272 absolute error = 9.43523187045877712303e-12 relative error = 5.1015750967124410574509791326268e-09 % glob_h = 0.01 y2(analytic)= = 0.9827484160758619756776290970863 y2(numeric) = = 0.9827484160385609597608790820021 absolute error = 3.730101591675001508420e-11 relative error = 3.7955813824349742893945871862238e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.05 y1(analytic)= = -0.19476549993116066542920847258421 y1(numeric) = = -0.19476549992134054902637305701899 absolute error = 9.82011640283541556522e-12 relative error = 5.0420204842779182737804792858908e-09 % glob_h = 0.01 y2(analytic)= = 0.98084983562039967078398926833319 y2(numeric) = = 0.98084983558314801321776683430003 absolute error = 3.725165756622243403316e-11 relative error = 3.7978960910627363451092170949486e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.06 y1(analytic)= = -0.20456409661936489475154871676555 y1(numeric) = = -0.20456409660915993868679460906642 absolute error = 1.020495606475410769913e-11 relative error = 4.9886349723151094673581285657096e-09 % glob_h = 0.01 y2(analytic)= = 0.97885317099874746436225936413382 y2(numeric) = = 0.97885317096154913732411428707839 absolute error = 3.719832703814507705543e-11 relative error = 3.8001947728473646482433952341262e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.07 y1(analytic)= = -0.2143422370683766998679641996429 y1(numeric) = = -0.21434223705778699001263828624009 absolute error = 1.058970985532591340281e-11 relative error = 4.9405614125169928845992230310758e-09 % glob_h = 0.01 y2(analytic)= = 0.97675862187570363999465209708169 y2(numeric) = = 0.97675862183856261968794754955718 absolute error = 3.714102030670454752451e-11 relative error = 3.8024768325444981654238685972290e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.08 y1(analytic)= = -0.22409894347229960281066703930354 y1(numeric) = = -0.22409894346132526612187888032436 absolute error = 1.097433668878815897918e-11 relative error = 4.8970943453576226090420753119842e-09 % glob_h = 0.01 y2(analytic)= = 0.97456639770443505027924932643519 y2(numeric) = = 0.97456639766735531650990490267619 absolute error = 3.707973376934442375900e-11 relative error = 3.8047416632345153503787792415667e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.09 y1(analytic)= = -0.23383324016862377285738488110394 y1(numeric) = = -0.23383324015726497745851083366977 absolute error = 1.135879539887404743417e-11 relative error = 4.8576478650695249024319888458396e-09 % glob_h = 0.01 y2(analytic)= = 0.97227671770553197468846614711665 y2(numeric) = = 0.9722767176685175104404073250506 absolute error = 3.701446424805882206605e-11 relative error = 3.8069886457230981802595331288262e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.1 y1(analytic)= = -0.24354415373579146446505176810215 y1(numeric) = = -0.24354415372404841972185212910687 absolute error = 1.174304474319963899528e-11 relative error = 4.8217313218444425104759866208562e-09 % glob_h = 0.01 y2(analytic)= = 0.96988981084508624322431993609985 y2(numeric) = = 0.96988981080814103423367908831912 absolute error = 3.694520899064084778073e-11 relative error = 3.8092171479201000873610003241257e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.11 y1(analytic)= = -0.25323071309053836186243493697733 y1(numeric) = = -0.25323071307841131845476720083975 absolute error = 1.212704340766773613758e-11 relative error = 4.7889307184203666142168400220870e-09 % glob_h = 0.01 y2(analytic)= = 0.96740591581179481803987065988796 y2(numeric) = = 0.96740591577492285236798494349537 absolute error = 3.687196567188571639259e-11 relative error = 3.8114265241953532376091545102815e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.12 y1(analytic)= = -0.26289194958500109624835579352512 y1(numeric) = = -0.2628919495724903462374675887607 absolute error = 1.251075001088820476442e-11 relative error = 4.7588943026355747869256128883023e-09 % glob_h = 0.01 y2(analytic)= = 0.96482528099309112264959001400351 y2(numeric) = = 0.96482528095629639025484168234454 absolute error = 3.679473239474833165897e-11 relative error = 3.8136161147099761494486360637154e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.13 y1(analytic)= = -0.27252689710358122492470790688738 y1(numeric) = = -0.2725268970906871018160936462672 absolute error = 1.289412310861426062018e-11 relative error = 4.7313212918259220743937050295246e-09 % glob_h = 0.01 y2(analytic)= = 0.96214816445030650557584786488685 y2(numeric) = = 0.96214816441359299788439275244388 absolute error = 3.671350769145511244297e-11 relative error = 3.8157852447216625616493996116326e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.14 y1(analytic)= = -0.28213459215955598604707843426133 y1(numeric) = = -0.28213459214627886484888418676938 absolute error = 1.327712119819424749195e-11 relative error = 4.7059529625795116394641037841298e-09 % glob_h = 0.01 y2(analytic)= = 0.95937483389286432226445263425997 y2(numeric) = = 0.95937483385623603173988276937737 absolute error = 3.662829052456986488260e-11 relative error = 3.8179332238623463326614170437385e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=217.4MB, alloc=4.4MB, time=11.76 x[1] = = 8.15 y1(analytic)= = -0.29171407399142616799800660787536 y1(numeric) = = -0.29171407397776646527496817658758 absolute error = 1.365970272303843128778e-11 relative error = 4.6825655465083616744253658082856e-09 % glob_h = 0.01 y2(analytic)= = 0.95650556665150921583954921186337 y2(numeric) = = 0.95650556661497013555153571046723 absolute error = 3.653908028801350139614e-11 relative error = 3.8200593453865445368884248442719e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.16 y1(analytic)= = -0.30126438465899145867623158189445 y1(numeric) = = -0.301264384644949632599131250235 absolute error = 1.404182607710033165945e-11 relative error = 4.6609645189206878128126023091005e-09 % glob_h = 0.01 y2(analytic)= = 0.95354064965057427374749004843324 y2(numeric) = = 0.95354064961412839693945263547769 absolute error = 3.644587680803741295555e-11 relative error = 3.8221628853885813233418984141772e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.17 y1(analytic)= = -0.3107845691391436672470632386696 y1(numeric) = = -0.31078456912472021763769112819956 absolute error = 1.442344960937211047004e-11 relative error = 4.6409799718577664456034753510598e-09 % glob_h = 0.01 y2(analytic)= = 0.95048037937928883355090441604859 y2(numeric) = = 0.95048037934294015320675411003255 absolute error = 3.634868034415030601604e-11 relative error = 3.8242431019867879842223852904153e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.18 y1(analytic)= = -0.32027367542136823911152833595062 y1(numeric) = = -0.32027367540656370748313480186104 absolute error = 1.480453162839353408958e-11 relative error = 4.6224628386694422583104291169518e-09 % glob_h = 0.01 y2(analytic)= = 0.94732506186212980706847634678433 y2(numeric) = = 0.94732506182588231547847802631107 absolute error = 3.624749158999832047326e-11 relative error = 3.8262992344726594607886419664909e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.19 y1(analytic)= = -0.32973075460294451402237941097387 y1(numeric) = = -0.32973075458775948361560538673687 absolute error = 1.518503040677402423700e-11 relative error = 4.6052817927340591082500314964216e-09 % glob_h = 0.01 y2(analytic)= = 0.94407501262821948770331012435012 y2(numeric) = = 0.9440750125920771760291118743192 absolute error = 3.614231167419825003092e-11 relative error = 3.8283305024228235543014011347574e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.2 y1(analytic)= = -0.33915486098383520740048812451964 y1(numeric) = = -0.33915486096827030321476081464635 absolute error = 1.556490418572730987329e-11 relative error = 4.5893206839424200508733950020257e-09 % glob_h = 0.01 y2(analytic)= = 0.94073055667977290115364874994565 y2(numeric) = = 0.94073055664373975899252505854565 absolute error = 3.603314216112369140000e-11 relative error = 3.8303361047715457152280276017052e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.21 y1(analytic)= = -0.34854505216125562598256570978725 y1(numeric) = = -0.34854505214531151480294751929699 absolute error = 1.594411117961819049026e-11 relative error = 4.5744764072110798245923719439405e-09 % glob_h = 0.01 y2(analytic)= = 0.93729202845959785474458052372378 y2(numeric) = = 0.93729202842367786969293656990904 absolute error = 3.591998505164395381474e-11 relative error = 3.8323152188413486945708968526403e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.22 y1(analytic)= = -0.35790038912391316095745317105734 y1(numeric) = = -0.357900389107590551376932252027 absolute error = 1.632260958052091903034e-11 relative error = 4.5606571204005214512411588893138e-09 % glob_h = 0.01 y2(analytic)= = 0.93375977181765093534871736925765 y2(numeric) = = 0.93375977178184809256490180381606 absolute error = 3.580284278381556544159e-11 relative error = 3.8342669993291717273829553996627e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.23 y1(analytic)= = -0.36721993634590763472020025229276 y1(numeric) = = -0.36721993632920727715741154167456 absolute error = 1.670035756278871061820e-11 relative error = 4.5477807465925787333618365624789e-09 % glob_h = 0.01 y2(analytic)= = 0.9301341399766528002681829243461 y2(numeric) = = 0.93013413994097108203465670597371 absolute error = 3.568171823352621837239e-11 relative error = 3.8361905772453273727327773388493e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.24 y1(analytic)= = -0.37650276188028311128750779590891 y1(numeric) = = -0.37650276186320579799987391462681 absolute error = 1.707731328763388128210e-11 relative error = 4.5357737091617852316705432927450e-09 % glob_h = 0.01 y2(analytic)= = 0.9264154954967661995201683705964 y2(numeric) = = 0.92641549546120958480507737156261 absolute error = 3.555661471509099903379e-11 relative error = 3.8380850588023346644073804758510e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.25 y1(analytic)= = -0.38574793745222181527145152962495 y1(numeric) = = -0.38574793743476838036373341073049 absolute error = 1.745343490771811889446e-11 relative error = 4.5245698584920823431810497295144e-09 % glob_h = 0.01 y2(analytic)= = 0.92260421023934026169439256288892 y2(numeric) = = 0.92260421020391272571259180687951 absolute error = 3.542753598180075600941e-11 relative error = 3.8399495242505137462071886915520e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.26 y1(analytic)= = -0.39495453855187084009725124929037 y1(numeric) = = -0.39495453853404215952549886262436 absolute error = 1.782868057175238666601e-11 relative error = 4.5141095572980433330883715571621e-09 % glob_h = 0.01 y2(analytic)= = 0.91870066532972466892366771830231 y2(numeric) = = 0.91870066529443018269724525584279 absolute error = 3.529448622642246245952e-11 relative error = 3.8417830266570184853528417415506e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.27 y1(analytic)= = -0.40412164452679236287161895309862 y1(numeric) = = -0.4041216445085893544425129954118 absolute error = 1.820300842910595768682e-11 relative error = 4.5043388978634968571540914113550e-09 % glob_h = 0.01 y2(analytic)= = 0.91470525111915743951908552369939 y2(numeric) = = 0.91470525108399996943743408816512 absolute error = 3.515747008165143553427e-11 relative error = 3.8435845906247583737038602198735e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.28 y1(analytic)= = -0.41324833867402812095724068129238 y1(numeric) = = -0.4132483386554517443228166040713 absolute error = 1.857637663442407722108e-11 relative error = 4.4952090295218814083393720061443e-09 % glob_h = 0.01 y2(analytic)= = 0.91061836714573012945980006809282 y2(numeric) = = 0.91061836711071363683928478768244 absolute error = 3.501649262051528041038e-11 relative error = 3.8453532109474179096894658918839e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.29 y1(analytic)= = -0.42233370833176894388245475458754 y1(numeric) = = -0.42233370831282020053020100685762 absolute error = 1.894874335225374772992e-11 relative error = 4.4866755786796803695106451496690e-09 % glob_h = 0.01 y2(analytic)= = 0.90644042209443435618472973116854 y2(numeric) = = 0.9064404220595627968280002993316 absolute error = 3.487155935672943183694e-11 relative error = 3.8470878511965190352909497574539e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=11.96 NO POLE NO POLE x[1] = = 8.3 y1(analytic)= = -0.43137684497062017370932646544651 y1(numeric) = = -0.43137684495130010694764933552667 absolute error = 1.932006676167712991984e-11 relative error = 4.4786981468588013006286256494056e-09 % glob_h = 0.01 y2(analytic)= = 0.90217183375629364000050440525296 y2(numeric) = = 0.90217183372157096375550023389966 absolute error = 3.472267624500417135330e-11 relative error = 3.8487874422361883593111047808645e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.31 y1(analytic)= = -0.44037684428445384739413667819035 y1(numeric) = = -0.44037684426476354233318462669873 absolute error = 1.969030506095205149162e-11 relative error = 4.4712398747817534297017949469595e-09 % glob_h = 0.01 y2(analytic)= = 0.8978130289865846498874605706974 y2(numeric) = = 0.89781302895201480020615756705771 absolute error = 3.456984968130300363969e-11 relative error = 3.8504508806609839370288341800472e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.32 y1(analytic)= = -0.44933280628083855599775818869017 y1(numeric) = = -0.44933280626077913952559907499217 absolute error = 2.005941647215911369800e-11 relative error = 4.4642670625793858780853220831214e-09 % glob_h = 0.01 y2(analytic)= = 0.89336444366215203154428811272915 y2(numeric) = = 0.89336444362773894504123583194935 absolute error = 3.441308650305228077980e-11 relative error = 3.8520770271518042147848847826486e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.33 y1(analytic)= = -0.45824383537103793783535677081683 y1(numeric) = = -0.45824383535061057858950188650987 absolute error = 2.042735924585488430696e-11 relative error = 4.4577488378681504673280400996186e-09 % glob_h = 0.01 y2(analytic)= = 0.8888265226378210861529535570277 y2(numeric) = = 0.88882652260356869216365158847557 absolute error = 3.425239398930196855213e-11 relative error = 3.8536647047445420936297567919396e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.34 y1(analytic)= = -0.46710904045956880579110043384034 y1(numeric) = = -0.46710904043877471412536976972832 absolute error = 2.079409166573066411202e-11 relative error = 4.4516568648023249176531486081258e-09 % glob_h = 0.01 y2(analytic)= = 0.88419971970191265855970058508235 y2(numeric) = = 0.88419971966782487869886313085834 absolute error = 3.408777986083745422401e-11 relative error = 3.8552126970057573937462146878622e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.35 y1(analytic)= = -0.47592753503330995305977694384341 y1(numeric) = = -0.47592753501215038100650063111182 absolute error = 2.115957205327631273159e-11 relative error = 4.4459650883186163724729644696723e-09 % glob_h = 0.01 y2(analytic)= = 0.87948449753086468334623892633346 y2(numeric) = = 0.87948449749694543106599662563568 absolute error = 3.391925228024230069778e-11 relative error = 3.8567197461092185266848913192290e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.36 y1(analytic)= = -0.48469843725015272650900253799085 y1(numeric) = = -0.484698437228628967736553919895 absolute error = 2.152375877244861809585e-11 relative error = 4.4406495087047727111025086859291e-09 % glob_h = 0.01 y2(analytic)= = 0.87468132764296492659869925598494 y2(numeric) = = 0.87468132760921810674678739873343 absolute error = 3.374681985191185725151e-11 relative error = 3.8581845508067058331489119850218e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.37 y1(analytic)= = -0.4934208700271845026785608423343 y1(numeric) = = -0.49342087000529789244421714960074 absolute error = 2.188661023434369273356e-11 relative error = 4.4356879823785874754705230655545e-09 % glob_h = 0.01 y2(analytic)= = 0.86979069035119955006162128299257 y2(numeric) = = 0.86979069031762905843960364046446 absolute error = 3.357049162201764252811e-11 relative error = 3.8596057642859714271930490592123e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.38 y1(analytic)= = -0.50209396112839624814275804430612 y1(numeric) = = -0.50209396110614816324088516556555 absolute error = 2.224808490187287874057e-11 relative error = 4.4310600453893059051027581592000e-09 % glob_h = 0.01 y2(analytic)= = 0.86481307471522221278126689718996 y2(numeric) = = 0.8648130746818319357028444763368 absolute error = 3.339027707842242085316e-11 relative error = 3.8609819919082097521050967589962e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.39 y1(analytic)= = -0.51071684325190539355284747438884 y1(numeric) = = -0.51071684322929725225840583224993 absolute error = 2.260814129444164213891e-11 relative error = 4.4267467566740163883575712904697e-09 % glob_h = 0.01 y2(analytic)= = 0.85974897849244851328806842902614 y2(numeric) = = 0.85974897845924232713752253061984 absolute error = 3.320618615054589840630e-11 relative error = 3.8623117888168052493715021736528e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.4 y1(analytic)= = -0.51928865411668529914480484058546 y1(numeric) = = -0.51928865409371856115217390436584 absolute error = 2.296673799263093621962e-11 relative error = 4.4227305585363819323930626035962e-09 % glob_h = 0.01 y2(analytic)= = 0.85459890808828066283323928142241 y2(numeric) = = 0.85459890805526243362405831019306 absolute error = 3.301822920918097122935e-11 relative error = 3.8635936574084839737949674838220e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.41 y1(analytic)= = -0.52780853654879263883817765184212 y1(numeric) = = -0.52780853652546880519529713943891 absolute error = 2.332383364288051240321e-11 relative error = 4.4189951521794623453064397388642e-09 % glob_h = 0.01 y2(analytic)= = 0.84936337850546736717074397198056 y2(numeric) = = 0.84936337847264095010448350945168 absolute error = 3.282641706626046252888e-11 relative error = 3.8648260446572995610391794213578e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.42 y1(analytic)= = -0.53627563856708408025945485937641 y1(numeric) = = -0.53627563854340469329728120322567 absolute error = 2.367938696217365615074e-11 relative error = 4.4155253864308329114282777033023e-09 % glob_h = 0.01 y2(analytic)= = 0.84404291329260398085424943068977 y2(numeric) = = 0.84404291325997321987967513847067 absolute error = 3.263076097457429221910e-11 relative error = 3.8660073392811250160033011411785e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.43 y1(analytic)= = -0.54468911346841368909338470753195 y1(numeric) = = -0.54468911344438033235066188301696 absolute error = 2.403335674272282451499e-11 relative error = 4.4123071580567783042516518767910e-09 % glob_h = 0.01 y2(analytic)= = 0.83863804449177808399071146297154 y2(numeric) = = 0.83863804445934681136327443581832 absolute error = 3.243127262743702715322e-11 relative error = 3.8671358687394940638556771088464e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=12.16 NO POLE NO POLE x[1] = = 8.44 y1(analytic)= = -0.55304811991230253809280326267449 y1(numeric) = = -0.55304811988791683623614760163936 absolute error = 2.438570185665566103513e-11 relative error = 4.4093273222812020740530091857036e-09 % glob_h = 0.01 y2(analytic)= = 0.83314931258536571684929247880635 y2(numeric) = = 0.83314931255313775269098671279969 absolute error = 3.222796415830576600666e-11 relative error = 3.8682098960507323109218818359088e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.45 y1(analytic)= = -0.56135182200507205385663040959186 y1(numeric) = = -0.56135182198033567259592954674106 absolute error = 2.473638126070086285080e-11 relative error = 4.4065736123107050437170464784570e-09 % glob_h = 0.01 y2(analytic)= = 0.82757726644198359265781327279776 y2(numeric) = = 0.82757726640996274451746495449459 absolute error = 3.202084814034831830317e-11 relative error = 3.8692276164153314327546116617551e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.46 y1(analytic)= = -0.56959938938343268811146640440998 y1(numeric) = = -0.56959938935834733411059303026803 absolute error = 2.508535400087337414195e-11 relative error = 4.4040345668255037431251169666514e-09 % glob_h = 0.01 y2(analytic)= = 0.82192246326160269332041953745898 y2(numeric) = = 0.82192246322979275573445789484398 absolute error = 3.180993758596164261500e-11 relative error = 3.8701871536314403886245008091725e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.47 y1(analytic)= = -0.57778999729751955469931781824696 y1(numeric) = = -0.57778999727208697548215943895778 absolute error = 2.543257921715837928918e-11 relative error = 4.4016994645309622144782863671538e-09 % glob_h = 0.01 y2(analytic)= = 0.8161854685198287366511528252971 y2(numeric) = = 0.81618546848823349070491231077818 absolute error = 3.159524594624051451892e-11 relative error = 3.8710865562871666049682477103622e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.48 y1(analytic)= = -0.58592282669336672877695023251364 y1(numeric) = = -0.58592282666758871262875666401653 absolute error = 2.577801614819356849711e-11 relative error = 4.3995582649801896051376758135250e-09 % glob_h = 0.01 y2(analytic)= = 0.81036685591135508703026981340303 y2(numeric) = = 0.81036685587997829991987341295115 absolute error = 3.137678711039640045188e-11 relative error = 3.8719237937130864010893408012724e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.49 y1(analytic)= = -0.59399706429481196086567610416197 y1(numeric) = = -0.59399706426869033672972695613345 absolute error = 2.612162413594914802852e-11 relative error = 4.3976015549774657898362052727182e-09 % glob_h = 0.01 y2(analytic)= = 0.80446720729259376414512182124261 y2(numeric) = = 0.80446720726143918873999530206075 absolute error = 3.115457540512651918186e-11 relative error = 3.8726967516769456063362647015829e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.5 y1(analytic)= = -0.602011902684823615348426522957 y1(numeric) = = -0.602011902658360252718021456295 absolute error = 2.646336263040506666200e-11 relative error = 4.3958204999577316977965966845145e-09 % glob_h = 0.01 y2(analytic)= = 0.79848711262349028666691316033911 y2(numeric) = = 0.79848711259256166107298008214835 absolute error = 3.092862559393307819076e-11 relative error = 3.8734032278009748643229490757817e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.51 y1(analytic)= = -0.60996654038624170078802937643651 y1(numeric) = = -0.60996654035943850959380444692745 absolute error = 2.680319119422492950906e-11 relative error = 4.3942067998111290546078573271259e-09 % glob_h = 0.01 y2(analytic)= = 0.79242716990852816933048317136808 y2(numeric) = = 0.79242716987782921645409049351168 absolute error = 3.069895287639267785640e-11 relative error = 3.8740409266805344411551409903473e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.52 y1(analytic)= = -0.61786018194192491803094606239347 y1(numeric) = = -0.61786018191478384852351999248425 absolute error = 2.714106950742606990922e-11 relative error = 4.3927526486853565537974429245802e-09 % glob_h = 0.01 y2(analytic)= = 0.78628798513692897291824121523656 y2(numeric) = = 0.78628798510646340003086533331774 absolute error = 3.046557288737588191882e-11 relative error = 3.8746074546809235202178248935282e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.53 y1(analytic)= = -0.62569203799429571145844535933286 y1(numeric) = = -0.6256920379668187540864001095698 absolute error = 2.747695737204524976306e-11 relative error = 4.3914506983539002268803399377313e-09 % glob_h = 0.01 y2(analytic)= = 0.78007017222205388709342309907839 y2(numeric) = = 0.78007017219182538539720614075586 absolute error = 3.022850169621695832253e-11 relative error = 3.8751003143871199635696288471140e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.54 y1(analytic)= = -0.63346132536427536894637665926708 y1(numeric) = = -0.633461325336464554229577200903 absolute error = 2.781081471679945836408e-11 relative error = 4.3902940247862327834235533465398e-09 % glob_h = 0.01 y2(analytic)= = 0.77377435294001290587388709887913 y2(numeric) = = 0.77377435291002515006805329874036 absolute error = 2.998775580583380013877e-11 relative error = 3.8755168986789369728120137725003e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.55 y1(analytic)= = -0.64116726712960127708932561622934 y1(numeric) = = -0.64116726710145867548758433667902 absolute error = 2.814260160174127955032e-11 relative error = 4.3892760975979021201119121704849e-09 % glob_h = 0.01 y2(analytic)= = 0.76740115686748773477774334921987 y2(numeric) = = 0.76740115683774438262594530732813 absolute error = 2.974335215179804189174e-11 relative error = 3.8758544844015689261905732370135e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.56 y1(analytic)= = -0.64880909270251850002889395674611 y1(numeric) = = -0.64880909267404622180598565992996 absolute error = 2.847227822290829681615e-11 relative error = 4.3883907520949228512238619621046e-09 % glob_h = 0.01 y2(analytic)= = 0.76095122131877464729828796586919 y2(numeric) = = 0.76095122128927933919693257363183 absolute error = 2.949530810135539223736e-11 relative error = 3.8761102255987227776344940620446e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.57 y1(analytic)= = -0.65638603790683791279296339083496 y1(numeric) = = -0.65638603787803810787599738493109 absolute error = 2.879980491696600590387e-11 relative error = 4.3876321636587912320130414359896e-09 % glob_h = 0.01 y2(analytic)= = 0.75442519128205358637013029642097 y2(numeric) = = 0.75442519125280994491773408684744 absolute error = 2.924364145239620957353e-11 relative error = 3.8762811462724631609868023915309e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=228.8MB, alloc=4.4MB, time=12.35 x[1] = = 8.58 y1(analytic)= = -0.66389734505435318339682459420267 y1(numeric) = = -0.66389734502522804123098088986944 absolute error = 2.912514216584370433323e-11 relative error = 4.3869948242463950493427796610513e-09 % glob_h = 0.01 y2(analytic)= = 0.74782371935488988386325778117132 y2(numeric) = = 0.74782371932590151343088142837573 absolute error = 2.898837043237635279559e-11 relative error = 3.8763641326305041452129474399938e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.59 y1(analytic)= = -0.67134226302060896207164175489406 y1(numeric) = = -0.6713422629911607114702789275686 absolute error = 2.944825060136282732546e-11 relative error = 4.3864735208036233317363743215839e-09 % glob_h = 0.01 y2(analytic)= = 0.74114746567897504787934062982178 y2(numeric) = = 0.74114746565024553418215228477281 absolute error = 2.872951369718834504897e-11 relative error = 3.8763559247779192704565838843852e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.6 y1(analytic)= = -0.67872004732001270086446978516048 y1(numeric) = = -0.67872004729024360985461258552386 absolute error = 2.976909100985719963662e-11 relative error = 4.3860633154130542366816191691148e-09 % glob_h = 0.01 y2(analytic)= = 0.73439709787411314371716418756345 y2(numeric) = = 0.73439709784564605338718129359049 absolute error = 2.846709032998289397296e-11 relative error = 3.8762531078060696737588121105327e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.61 y1(analytic)= = -0.68602996018028259249045717118302 y1(numeric) = = -0.68602996015019496815367249825058 absolute error = 3.008762433678467293244e-11 relative error = 4.3857595270151046984507727486174e-09 % glob_h = 0.01 y2(analytic)= = 0.72757329097145936981408128148062 y2(numeric) = = 0.72757329094325824997414046390686 absolute error = 2.820111983994081757376e-11 relative error = 3.8760521022269174075646645274259e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.62 y1(analytic)= = -0.69327127061622418370538898260983 y1(numeric) = = -0.69327127058582037201405936409436 absolute error = 3.040381169132961851547e-11 relative error = 4.3855577145587976389099949649594e-09 % glob_h = 0.01 y2(analytic)= = 0.72067672734601750475025606743867 y2(numeric) = = 0.72067672731808588258926063692751 absolute error = 2.793162216099543051116e-11 relative error = 3.8757491536957401982488096673877e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.63 y1(analytic)= = -0.70044325450282828559871309381536 y1(numeric) = = -0.70044325447211067124771734836317 absolute error = 3.071761435099574545219e-11 relative error = 4.3854536614531295051317943789051e-09 % glob_h = 0.01 y2(analytic)= = 0.71370809664840297551474701308181 y2(numeric) = = 0.71370809662074435786424156185071 absolute error = 2.765861765050545123110e-11 relative error = 3.8753403219595296943628383068953e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.64 y1(analytic)= = -0.70754519464768287107693503645444 y1(numeric) = = -0.70754519461665387731074632200851 absolute error = 3.102899376618871444593e-11 relative error = 4.3854433612031500809878435785670e-09 % glob_h = 0.01 y2(analytic)= = 0.7066680957358783706697384884108 y2(numeric) = = 0.7066680957084962435818599923865 absolute error = 2.738212708787849602430e-11 relative error = 3.8748214689619633856742148777299e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.65 y1(analytic)= = -0.71457638086269171840797619058494 y1(numeric) = = -0.71457638083135380684318817242584 absolute error = 3.133791156478801815910e-11 relative error = 4.3855230041265112056494086604233e-09 % glob_h = 0.01 y2(analytic)= = 0.69955742860266829480413432665275 y2(numeric) = = 0.69955742857556612313098909491306 absolute error = 2.710217167314523173969e-11 relative error = 3.8741882460287059520503865656957e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.66 y1(analytic)= = -0.72153611003509262902190621560862 y1(numeric) = = -0.7215361100034482994651986165031 absolute error = 3.164432955670759910552e-11 relative error = 4.3856889650565853934819720065276e-09 % glob_h = 0.01 y2(analytic)= = 0.69237680630956053273299723501445 y2(numeric) = = 0.69237680628274175970751297048528 absolute error = 2.681877302548426452917e-11 relative error = 3.8734360800488217343171287879199e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.67 y1(analytic)= = -0.72842368619776811780545129868205 y1(numeric) = = -0.7284236861658199080670066219701 absolute error = 3.194820973844467671195e-11 relative error = 4.3859377919474587338854794362103e-09 % glob_h = 0.01 y2(analytic)= = 0.68512694691280056326774861042967 y2(numeric) = = 0.68512694688626861008605076278302 absolute error = 2.653195318169784764665e-11 relative error = 3.8725601585591550659050583974230e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.68 y1(analytic)= = -0.73523842059884154487984081637764 y1(numeric) = = -0.73523842056659203058222456069231 absolute error = 3.224951429761625568533e-11 relative error = 4.3862661953043029822662825782821e-09 % glob_h = 0.01 y2(analytic)= = 0.67780857539228653304649736597555 y2(numeric) = = 0.6778085753660447984518588690064 absolute error = 2.624173459463849696915e-11 relative error = 3.8715554136285316930451421675989e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.69 y1(analytic)= = -0.7419796317705517293068112080879 y1(numeric) = = -0.74197963173800352368932841966755 absolute error = 3.254820561748278842035e-11 relative error = 4.3866710383699493868166986346549e-09 % glob_h = 0.01 y2(analytic)= = 0.67042242357907187086727741272543 y2(numeric) = = 0.67042242355312373073569080417562 absolute error = 2.594814013158660854981e-11 relative error = 3.8704165044274056578305020599556e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.7 y1(analytic)= = -0.74864664559739915731879178088928 y1(numeric) = = -0.74864664556455491103733331604931 absolute error = 3.284424628145846483997e-11 relative error = 4.3871493280050258856300543454108e-09 % glob_h = 0.01 y2(analytic)= = 0.66296923008218279220234618661559 y2(numeric) = = 0.6629692300565315991297670084637 absolute error = 2.565119307257917815189e-11 relative error = 3.8691377983559527604387755874273e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.71 y1(analytic)= = -0.75523879538355697050923774484887 y1(numeric) = = -0.75523879535041937143163014106935 absolute error = 3.313759907760760377952e-11 relative error = 4.3876982062048708004615189516692e-09 % glob_h = 0.01 y2(analytic)= = 0.65544974021475801208210758085277 y2(numeric) = = 0.65544974018940709497341785250478 absolute error = 2.535091710868972834799e-11 relative error = 3.8677133505893989740891392548282e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.72 y1(analytic)= = -0.76175542191953999294046708170996 y1(numeric) = = -0.76175542188611176593734046090674 absolute error = 3.342822700312662080322e-11 relative error = 4.3883149422016794408205747147347e-09 % glob_h = 0.01 memory used=232.7MB, alloc=4.4MB, time=12.56 y2(analytic)= = 0.64786470591951805231582085747297 y2(numeric) = = 0.64786470589447071597556130307315 absolute error = 2.504733634025955439982e-11 relative error = 3.8661368818833444312516860633520e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.73 y1(analytic)= = -0.76819587354812513032184780066808 y1(numeric) = = -0.76819587351440903705303675248786 absolute error = 3.371609326881104818022e-11 relative error = 4.3889969251050445391635268402844e-09 % glob_h = 0.01 y2(analytic)= = 0.64021488569357159605626476354024 y2(numeric) = = 0.64021488566883112078118435778077 absolute error = 2.474047527508040575947e-11 relative error = 3.8644017544637395978398008538312e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.74 y1(analytic)= = -0.77455950622951654927335124538182 y1(numeric) = = -0.77455950619551538796984416173636 absolute error = 3.400116130350708364546e-11 relative error = 4.3897416570382779695961688070222e-09 % glob_h = 0.01 y2(analytic)= = 0.63250104451256640901023922324874 y2(numeric) = = 0.63250104448813605018371049759508 absolute error = 2.443035882652872565366e-11 relative error = 3.8625009458056868057528874098016e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.75 y1(analytic)= = -0.78084568360574912021084923192669 y1(numeric) = = -0.7808456835714657254523020863978 absolute error = 3.428339475854714552889e-11 relative error = 4.3905467467317030986411492558770e-09 % glob_h = 0.01 y2(analytic)= = 0.62472395375419241213957620079218 y2(numeric) = = 0.62472395373007539982792462396637 absolute error = 2.411701231165157682581e-11 relative error = 3.8604270200820247985857868049638e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.76 y1(analytic)= = -0.7870537770643236835625358448178 y1(numeric) = = -0.78705377702976092605036693196283 absolute error = 3.456275751216891285497e-11 relative error = 4.3914099035375312409795675014274e-09 % glob_h = 0.01 y2(analytic)= = 0.61688439112104455548164240598992 y2(numeric) = = 0.61688439109724409403243801887159 absolute error = 2.380046144920438711833e-11 relative error = 3.8581720970362953880860401189189e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.77 y1(analytic)= = -0.79318316580106777584288146067107 y1(numeric) = = -0.79318316576622856216896413057884 absolute error = 3.483921367391733009223e-11 relative error = 4.3923289318340232814048438292998e-09 % glob_h = 0.01 y2(analytic)= = 0.60898314056285320673767106818545 y2(numeric) = = 0.60898314053937247438003041400926 absolute error = 2.348073235764065417619e-11 relative error = 3.8557278180047097050131892999437e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.78 y1(analytic)= = -0.79923323688221552956389536788292 y1(numeric) = = -0.79923323684710280197486631051184 absolute error = 3.511272758902905737108e-11 relative error = 4.3933017257894249139517854886199e-09 % glob_h = 0.01 y2(analytic)= = 0.60102099219808983152525615175655 y2(numeric) = = 0.60102099217493197997220239761214 absolute error = 2.315785155305375414441e-11 relative error = 3.8530853087775649519622978167060e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.79 y1(analytic)= = -0.80520338530570053904543893354847 y1(numeric) = = -0.80520338527031727520264008536291 absolute error = 3.538326384279884818556e-11 relative error = 4.3943262644586832068142019811872e-09 % glob_h = 0.01 y2(analytic)= = 0.59299874223495580466165538178754 y2(numeric) = = 0.59299874221212395871458437697354 absolute error = 2.283184594707100481400e-11 relative error = 3.8502351389515517491452918476801e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.8 y1(analytic)= = -0.81109301406165556288908550421932 y1(numeric) = = -0.81109301402600477562415816636674 absolute error = 3.565078726492733785258e-11 relative error = 4.3954006071882316652511340355409e-09 % glob_h = 0.01 y2(analytic)= = 0.58491719289176225353093131181238 y2(numeric) = = 0.58491719286925951068623117256858 absolute error = 2.250274284470013924380e-11 relative error = 3.8471672773797617550509032590919e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.81 y1(analytic)= = -0.81690153419211301319569590518449 y1(numeric) = = -0.81690153415619775026184617786533 absolute error = 3.591526293384972731916e-11 relative error = 4.3965228893061957110580474633970e-09 % glob_h = 0.01 y2(analytic)= = 0.57677715231670889548424381016098 y2(numeric) = = 0.57677715229453832554211545871304 absolute error = 2.217056994212835144794e-11 relative error = 3.8438710432750411588677038540745e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.82 y1(analytic)= = -0.82262836484990026152753802257161 y1(numeric) = = -0.82262836481372360534649317428613 absolute error = 3.617665618104484828548e-11 relative error = 4.3976913180772427477309401268400e-09 % glob_h = 0.01 y2(analytic)= = 0.56857943450706989132270318966342 y2(numeric) = = 0.56857943448523453599822910837251 absolute error = 2.183535532447408129091e-11 relative error = 3.8403350524635575394299896999137e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.83 y1(analytic)= = -0.82827293335672387213343351434744 y1(numeric) = = -0.82827293332028893953810941729984 absolute error = 3.643493259532409704760e-11 relative error = 4.3989041689030004515250994492897e-09 % glob_h = 0.01 y2(analytic)= = 0.56032485922779479621009079778453 y2(numeric) = = 0.56032485920629766874659908651271 absolute error = 2.149712746349171127182e-11 relative error = 3.8365471582177753229495371961124e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.84 y1(analytic)= = -0.8338346752604369540620125018894 y1(numeric) = = -0.83383467522374689603491277592975 absolute error = 3.669005802709972595965e-11 relative error = 4.4001597817505111370185308913333e-09 % glob_h = 0.01 y2(analytic)= = 0.55201425192953274785252348033209 y2(numeric) = = 0.5520142519083768326372941269235 absolute error = 2.115591521522935340859e-11 relative error = 3.8324943860199477043800236259270e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.85 y1(analytic)= = -0.83931303439148390547558755101105 y1(numeric) = = -0.83931303435454190688295556804046 absolute error = 3.694199859263198297059e-11 relative error = 4.4014565577925945732819621042221e-09 % glob_h = 0.01 y2(analytic)= = 0.54364844366608808945793100348531 y2(numeric) = = 0.54364844364527634164029109353762 absolute error = 2.081174781763990994769e-11 relative error = 3.8281628615169184034752946377528e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.86 y1(analytic)= = -0.84470746291851690573725268518084 y1(numeric) = = -0.84470746288132618505899809387617 absolute error = 3.719072067825459130467e-11 relative error = 4.4027929562452703509973526515698e-09 % glob_h = 0.01 y2(analytic)= = 0.53522827101131568184426373482397 y2(numeric) = = 0.53522827099085102695611813769616 absolute error = 2.046465488814559712781e-11 relative error = 3.8235377308223200644412083262442e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=12.76 NO POLE NO POLE x[1] = = 8.87 y1(analytic)= = -0.85001742140317859366834564328225 y1(numeric) = = -0.85001742136574240272376758025355 absolute error = 3.743619094457806302870e-11 relative error = 4.4041674913885561969113055873157e-09 % glob_h = 0.01 y2(analytic)= = 0.52675457597546421509596608685943 y2(numeric) = = 0.52675457595534954867480996014555 absolute error = 2.011466642115612671388e-11 relative error = 3.8186030722005632752232533112181e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.88 y1(analytic)= = -0.85524237885404545375409971539675 y1(numeric) = = -0.85524237881636707742342937341548 absolute error = 3.767837633067034198127e-11 relative error = 4.4055787297580215474558724928511e-09 % glob_h = 0.01 y2(analytic)= = 0.51822820592097588536783640114957 y2(numeric) = = 0.51822820590121407258229565565777 absolute error = 1.976181278554074549180e-11 relative error = 3.8133417980252130632942917944425e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.89 y1(analytic)= = -0.86038181277972651600381726342176 y1(numeric) = = -0.86038181274180927194560299009088 absolute error = 3.791724405821427333088e-11 relative error = 4.4070252874954461028616614549276e-09 % glob_h = 0.01 y2(analytic)= = 0.50965001347775085679842618490184 y2(numeric) = = 0.50965001345834473207637184652926 absolute error = 1.940612472205433837258e-11 relative error = 3.8077355457386889497038400685020e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.9 y1(analytic)= = -0.86543520924111205963982767822535 y1(numeric) = = -0.86543520920295929800418627934587 absolute error = 3.815276163564139887948e-11 relative error = 4.4085058278478198220167728070533e-09 % glob_h = 0.01 y2(analytic)= = 0.5010208564578849820161746471113 y2(numeric) = = 0.50102085643883734867545684091384 absolute error = 1.904763334071780619746e-11 relative error = 3.8017645563461528320763390029742e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.91 y1(analytic)= = -0.87040206290276709578840131881462 y1(numeric) = = -0.87040206286438219892615973967735 absolute error = 3.838489686224157913727e-11 relative error = 4.4100190588047318017938625438150e-09 % glob_h = 0.01 y2(analytic)= = 0.49234159776988930739517625804105 y2(numeric) = = 0.49234159775120293727702332327951 absolute error = 1.868637011815293476154e-11 relative error = 3.7954075387484470357773314762104e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.92 y1(analytic)= = -0.87528187708346448986717810160667 y1(numeric) = = -0.87528187704485087203493015644538 absolute error = 3.861361783224794516129e-11 relative error = 4.4115637308649378099894246712755e-09 % glob_h = 0.01 y2(analytic)= = 0.48361310533239994103857224794767 y2(numeric) = = 0.48361310531407757414370027096496 absolute error = 1.832236689487197698271e-11 relative error = 3.7886415179502910308603742249581e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.93 y1(analytic)= = -0.88007416380585267039898279189669 y1(numeric) = = -0.88007416376701377746008610672069 absolute error = 3.883889293889668517600e-11 relative error = 4.4131386349235762802480027299978e-09 % glob_h = 0.01 y2(analytic)= = 0.47483625198738691243085950224904 y2(numeric) = = 0.47483625196943125655833732671502 absolute error = 1.795565587252217553402e-11 relative error = 3.7814416648624233691797107781533e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.94 y1(analytic)= = -0.8847784438452529575225352353732 y1(numeric) = = -0.88477844380619226664407406229547 absolute error = 3.906069087846117307773e-11 relative error = 4.4147426002721260560732918791083e-09 % glob_h = 0.01 y2(analytic)= = 0.46601191541287070280082591304118 y2(numeric) = = 0.46601191539528443318974045441084 absolute error = 1.758626961108545863034e-11 relative error = 3.7737811050399048401577823424745e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.95 y1(analytic)= = -0.88939424677758163150786876353494 y1(numeric) = = -0.88939424673830265085360881546869 absolute error = 3.927898065425994806625e-11 relative error = 4.4163744927037712398677529858182e-09 % glob_h = 0.01 y2(analytic)= = 0.45714097803515517446933991118531 y2(numeric) = = 0.45714097801794093344330636417059 absolute error = 1.721424102603354701472e-11 relative error = 3.7656307032509636384251451371813e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.96 y1(analytic)= = -0.89392111102639194910954015514856 y1(numeric) = = -0.89392111098689821752890209830217 absolute error = 3.949373158063805684639e-11 relative error = 4.4180332127173637998182427303791e-09 % glob_h = 0.01 y2(analytic)= = 0.44822432694058567581592041826517 y2(numeric) = = 0.44822432692374607243048170274164 absolute error = 1.683960338543871552353e-11 relative error = 3.7569588202362089143027510891664e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.97 y1(analytic)= = -0.89835858390903140359519738237311 y1(numeric) = = -0.89835858386932649030827611027366 absolute error = 3.970491328692127209945e-11 relative error = 4.4197176938136572923943915708629e-09 % glob_h = 0.01 y2(analytic)= = 0.43926285378684114598005589400761 y2(numeric) = = 0.43926285377037875567301543608325 absolute error = 1.646239030704045792436e-11 relative error = 3.7477310373776969666968611819401e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.98 y1(analytic)= = -0.90270622168190961276196653991965 y1(numeric) = = -0.90270622164199711704062383668078 absolute error = 3.991249572134270323887e-11 relative error = 4.4214269008779289425701095929844e-09 % glob_h = 0.01 y2(analytic)= = 0.43025745471376909001287934758985 y2(numeric) = = 0.43025745469768645425761103857641 absolute error = 1.608263575526830901344e-11 relative error = 3.7379098442274201559320590459994e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 8.99 y1(analytic)= = -0.90696358958487230818957943282263 y1(numeric) = = -0.90696358954475585903463811498658 absolute error = 4.011644915494131783605e-11 relative error = 4.4231598286435157929309577579480e-09 % glob_h = 0.01 y2(analytic)= = 0.42120903025377234090738020563873 y2(numeric) = = 0.42120903023807196686915912240727 absolute error = 1.570037403822108323146e-11 relative error = 3.7274542829155004681293114494504e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9 y1(analytic)= = -0.91113026188467698836829471118117 y1(numeric) = = -0.91113026184436024418286281664982 absolute error = 4.031674418543189453135e-11 relative error = 4.4249155002311667646458568307487e-09 % glob_h = 0.01 y2(analytic)= = 0.41211848524175656975627256635244 y2(numeric) = = 0.41211848522644092995166977204601 absolute error = 1.531563980460279430643e-11 relative error = 3.7163195423321881957577549715248e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE memory used=240.3MB, alloc=4.4MB, time=12.96 NO POLE x[1] = = 9.01 y1(analytic)= = -0.91520582191756588817252934993107 y1(numeric) = = -0.91520582187705253643148341920037 absolute error = 4.051335174104593073070e-11 relative error = 4.4266929657594590520811754110888e-09 % glob_h = 0.01 y2(analytic)= = 0.40298672872464754921146056152928 y2(numeric) = = 0.40298672870971908117084503587007 absolute error = 1.492846804061552565921e-11 relative error = 3.7044564936072218404871290805705e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.02 y1(analytic)= = -0.91918986213093200741873046680308 y1(numeric) = = -0.91918986209022576433438743587234 absolute error = 4.070624308434303093074e-11 relative error = 4.4284913010218468197104900351245e-09 % glob_h = 0.01 y2(analytic)= = 0.39381467387048721844335285085761 y2(numeric) = = 0.39381467385594832437654332434631 absolute error = 1.453889406680952651130e-11 relative error = 3.6918111567348284818370954653895e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.03 y1(analytic)= = -0.92308198412407403193935326601151 y1(numeric) = = -0.92308198408317864212336096189769 absolute error = 4.089538981599230411382e-11 relative error = 4.4303096062262049692412437480561e-09 % glob_h = 0.01 y2(analytic)= = 0.38460323787711763991777729032715 y2(numeric) = = 0.38460323786297068638288647651309 absolute error = 1.414695353489081381406e-11 relative error = 3.6783240861354436289421160988466e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.04 y1(analytic)= = -0.92688179868803607171480003089944 y1(numeric) = = -0.92688179864695530783627672958992 absolute error = 4.108076387852330130952e-11 relative error = 4.4321470047930028684323190497427e-09 % glob_h = 0.01 y2(analytic)= = 0.37535334188046197951872163426432 y2(numeric) = = 0.37535334186670929709423506899014 absolute error = 1.375268242448656527418e-11 relative error = 3.6639296604068478660453143573699e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.05 y1(analytic)= = -0.93058892584452823212270664275207 y1(numeric) = = -0.93058892580326589456266061562218 absolute error = 4.126233756004602712989e-11 relative error = 4.4340026422084942611338837801914e-09 % glob_h = 0.01 y2(analytic)= = 0.36606591086241168184245573513161 y2(numeric) = = 0.36606591084905556480258714125135 absolute error = 1.335611703986859388026e-11 relative error = 3.6485552583694633334211740863781e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.06 y1(analytic)= = -0.93420299488392412627988539838816 y1(numeric) = = -0.93420299484248404278194583653584 absolute error = 4.144008349793956185232e-11 relative error = 4.4358756849295418187714206180174e-09 % glob_h = 0.01 y2(analytic)= = 0.35674187355832905186874539748448 y2(numeric) = = 0.35674187354537175786211019804471 absolute error = 1.295729400663519943977e-11 relative error = 3.6321202995859184179255870066617e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.07 y1(analytic)= = -0.9377236444023315287573544203177 y1(numeric) = = -0.9377236443607175540748455868716 absolute error = 4.161397468250883344610e-11 relative error = 4.4377653193369094993351922705730e-09 % glob_h = 0.01 y2(analytic)= = 0.3473821623641744926739098396967 y2(numeric) = = 0.34738216235161824240555814198269 absolute error = 1.255625026835169771401e-11 relative error = 3.6145351226147538251280257993487e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.08 y1(analytic)= = -0.94115052233773246363397426498015 y1(numeric) = = -0.94115052229594847917336518316415 absolute error = 4.178398446060908181600e-11 relative error = 4.4396707507340544632146437115952e-09 % glob_h = 0.01 y2(analytic)= = 0.33798771324326768638455774711486 y2(numeric) = = 0.3379877132311146633014078143252 absolute error = 1.215302308314993278966e-11 relative error = 3.5956996680535417563682044535613e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.09 y1(analytic)= = -0.94448328600518911291000300505808 y1(numeric) = = -0.94448328596323902637076544458964 absolute error = 4.195008653923756046844e-11 relative error = 4.4415912023886340415289565738470e-09 % glob_h = 0.01 y2(analytic)= = 0.3285594656326920421762077861611 y2(numeric) = = 0.32855946562094439215592070281175 absolute error = 1.174765002028708334935e-11 relative error = 3.5755019255540750282486277186978e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.1 y1(analytic)= = -0.94772160213111202471906658957537 y1(numeric) = = -0.9477216020889997697299745657823 absolute error = 4.211225498909202379307e-11 relative error = 4.4435259146141133329894293122117e-09 % glob_h = 0.01 y2(analytic)= = 0.31909836234935177079399768398541 y2(numeric) = = 0.31909836233801160183733360548626 absolute error = 1.134016895666407849915e-11 relative error = 3.5538160939380688654914738282541e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.11 y1(analytic)= = -0.95086514688658719454628002973121 y1(numeric) = = -0.95086514684431673029818447853751 absolute error = 4.227046424809555119370e-11 relative error = 4.4454741438890164870039424895215e-09 % glob_h = 0.01 y2(analytic)= = 0.30960534949569097980974429247879 y2(numeric) = = 0.3096053494847603617364403487012 absolute error = 1.093061807330394377759e-11 relative error = 3.5305003906129450622553175304619e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.12 y1(analytic)= = -0.95391360591975868677217007345807 y1(numeric) = = -0.95391360587733399764728281105965 absolute error = 4.242468912488726239842e-11 relative error = 4.4474351620115105871940253642749e-09 % glob_h = 0.01 y2(analytic)= = 0.30008137636508421762726177191286 y2(numeric) = = 0.30008137635456518177547136900416 absolute error = 1.051903585179040290870e-11 relative error = 3.5053944297405384731814015579150e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.13 y1(analytic)= = -0.95686667438726355830723040443788 y1(numeric) = = -0.9568666743446886535049519230097 absolute error = 4.257490480227848142818e-11 relative error = 4.4494082552871461688234467294388e-09 % glob_h = 0.01 y2(analytic)= = 0.290527395346907927102696411862 y2(numeric) = = 0.29052739533680246603202934609345 absolute error = 1.010546107066706576855e-11 relative error = 3.4783160667518158152697557924326e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.14 y1(analytic)= = -0.95972405698471594085094159243293 y1(numeric) = = -0.95972405694199485401026768252675 absolute error = 4.272108684067390990618e-11 relative error = 4.4513927237477035967469221350827e-09 % glob_h = 0.01 y2(analytic)= = 0.28094436183130230155540919763301 y2(numeric) = = 0.28094436182161236875361165972039 absolute error = 9.68993280179753791262e-12 relative error = 3.4490575780324855441624949090308e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=244.1MB, alloc=4.4MB, time=13.16 x[1] = = 9.15 y1(analytic)= = -0.96248546797623723339243321014104 y1(numeric) = = -0.96248546793337402221097583649418 absolute error = 4.286321118145737364686e-11 relative error = 4.4533878803992105380035649588532e-09 % glob_h = 0.01 y2(analytic)= = 0.27133323411363306690444017850455 y2(numeric) = = 0.27133323410436057649775338664771 absolute error = 9.27249040668679185684e-12 relative error = 3.4173810064135073890146859198012e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.16 y1(analytic)= = -0.96515063122302945195814646208581 y1(numeric) = = -0.96515063118002819780780475231308 absolute error = 4.300125415034170977273e-11 relative error = 4.4553930504973032618391896259308e-09 % glob_h = 0.01 y2(analytic)= = 0.26169497329866274367272607517005 y2(numeric) = = 0.26169497328980957013996193005016 absolute error = 8.85317353276414511989e-12 relative error = 3.3830124519282788485856925909517e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.17 y1(analytic)= = -0.96771928021098887929533360469841 y1(numeric) = = -0.96771928016785368683465123972909 absolute error = 4.313519246068236496932e-11 relative error = 4.4574075708482041083197206637382e-09 % glob_h = 0.01 y2(analytic)= = 0.25203054320444097165301368915069 y2(numeric) = = 0.2520305431960089495433854943343 absolute error = 8.43202210962819481639e-12 relative error = 3.3456350180495171482156776627243e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.18 y1(analytic)= = -0.97019115807735725314943710568076 y1(numeric) = = -0.97019115803409224993268282677776 absolute error = 4.326500321675427890300e-11 relative error = 4.4594307891336797504008914649534e-09 % glob_h = 0.01 y2(analytic)= = 0.24234091026592350812291139369661 y2(numeric) = = 0.24234091025791443177765733035642 absolute error = 8.00907634525406334019e-12 relative error = 3.3048800289087015593291667480528e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.19 y1(analytic)= = -0.97256601763640782803873005426767 y1(numeric) = = -0.97256601759301716412173842397452 absolute error = 4.339066391699163029315e-11 relative error = 4.4614620632584303506046840109356e-09 % glob_h = 0.01 y2(analytic)= = 0.23262704343832953762893996726429 y2(numeric) = = 0.23262704343074516090677665287135 absolute error = 7.58437672216331439294e-12 relative error = 3.2603160019845097442944143130086e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.2 y1(analytic)= = -0.9748436214041637419414453384758 y1(numeric) = = -0.97484362136065158948425531182761 absolute error = 4.351215245719002664819e-11 relative error = 4.4635007607184388553418537680350e-09 % glob_h = 0.01 y2(analytic)= = 0.22288991410024695752806905775828 y2(numeric) = = 0.22288991409308899353451215446302 absolute error = 7.15796399355690329526e-12 relative error = 3.2114346772719099969205186967392e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.21 y1(analytic)= = -0.97702374162214621607932344666553 y1(numeric) = = -0.97702374157851676894565272442078 absolute error = 4.362944713367072224475e-11 relative error = 4.4655462579888829102055916233058e-09 % glob_h = 0.01 y2(analytic)= = 0.2131304959564953286774397976603 y2(numeric) = = 0.21313049594976544949802826749464 absolute error = 6.72987917941153016566e-12 relative error = 3.1576331435860066155663231024606e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.22 y1(analytic)= = -0.97910616028015021299739063915486 y1(numeric) = = -0.97910616023640768635098418660479 absolute error = 4.374252664640645255007e-11 relative error = 4.4675979399302796139581315024474e-09 % glob_h = 0.01 y2(analytic)= = 0.20334976494075620489625732651694 y2(numeric) = = 0.20334976493445604133371755735225 absolute error = 6.30016356253976916469e-12 relative error = 3.0981907278699116920210870370067e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.23 y1(analytic)= = -0.98109066913804527539313916386911 y1(numeric) = = -0.98109066909419390529103068690989 absolute error = 4.385137010210847695922e-11 relative error = 4.4696551992115959193109591691862e-09 % glob_h = 0.01 y2(analytic)= = 0.1935486991179805780857659098894 y2(numeric) = = 0.19354869911211171940115155831034 absolute error = 5.86885868461435157906e-12 relative error = 3.0322387654162938882276678063912e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.24 y1(analytic)= = -0.98297706974659936562939390313786 y1(numeric) = = -0.98297706970264340861211947769766 absolute error = 4.395595701727442544020e-11 relative error = 4.4717174357491152656947794503482e-09 % glob_h = 0.01 y2(analytic)= = 0.18372827858658319818146779927678 y2(numeric) = = 0.18372827858114719183931081421548 absolute error = 5.43600634215698506130e-12 relative error = 2.9587205540573495224605301862763e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.25 y1(analytic)= = -0.98476517346732362356426730672485 y1(numeric) = = -0.98476517342326735624307075827251 absolute error = 4.405626732119654845234e-11 relative error = 4.4737840561599042953413909745668e-09 % glob_h = 0.01 y2(analytic)= = 0.17388948538043354842408614943551 y2(numeric) = = 0.17388948537543189984159405359108 absolute error = 5.00164858249209584443e-12 relative error = 2.8763375609224116091654758660104e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.26 y1(analytic)= = -0.98645480149133605823895685866475 y1(numeric) = = -0.98645480144718377688002688534025 absolute error = 4.415228135892997332450e-11 relative error = 4.4758544732287725348326144400744e-09 % glob_h = 0.01 y2(analytic)= = 0.16403330337065327677007098177607 y2(numeric) = = 0.16403330336608744907040509655759 absolute error = 4.56582769966588521848e-12 relative error = 2.7834760416601743744419373255590e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.27 y1(analytic)= = -0.98804578485724228706993598883439 y1(numeric) = = -0.98804578481299830717571541468386 absolute error = 4.424397989422057415053e-11 relative error = 4.4779281053876629715528794186942e-09 % glob_h = 0.01 y2(analytic)= = 0.15416071816722990361667194220025 y2(numeric) = = 0.154160718163101317386340846216 absolute error = 4.12858623033109598425e-12 relative error = 2.6781052134516545369500236318340e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.28 y1(analytic)= = -0.98953796446803153448651977649193 y1(numeric) = = -0.98953796442370019037412771031296 absolute error = 4.433134411239206617897e-11 relative error = 4.4800043762064527472689972430430e-09 % glob_h = 0.01 y2(analytic)= = 0.14427271702045664438881704250229 y2(numeric) = = 0.14427271701676667743921915351138 absolute error = 3.68996694959788899091e-12 relative error = 2.5576332281000038674445705277016e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.29 y1(analytic)= = -0.99093119110698620042802164114533 y1(numeric) = = -0.99093119106257184480482970150289 absolute error = 4.441435562319193964244e-11 relative error = 4.4820827138941809378168478505390e-09 % glob_h = 0.01 y2(analytic)= = 0.13437028872220820292340549005999 y2(numeric) = = 0.1343702887189581900565542558442 absolute error = 3.25001286685123421579e-12 relative error = 2.4186990277070712490107033898641e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=13.36 NO POLE NO POLE x[1] = = 9.3 y1(analytic)= = -0.99222532545260340775690923463516 y1(numeric) = = -0.99222532540811041129331338264705 absolute error = 4.449299646359585198811e-11 relative error = 4.4841625508097547776041599568211e-09 % glob_h = 0.01 y2(analytic)= = 0.12445442350706240798940627858634 y2(numeric) = = 0.12445442350425364076787105342926 absolute error = 2.80876722153522515708e-12 relative error = 2.2568641132919122040148527352245e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.31 y1(analytic)= = -0.99342023809252703644565280023839 y1(numeric) = = -0.99342023804795978734508269870329 absolute error = 4.456724910057010153510e-11 relative error = 4.4862433229812168916780719117004e-09 % glob_h = 0.01 y2(analytic)= = 0.11452611295327758069771216851111 y2(numeric) = = 0.11452611295091130721880743892814 absolute error = 2.36627347890472958297e-12 relative error = 2.0661431859388100124291997318123e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.32 y1(analytic)= = -0.99451580953648885134545730374623 y1(numeric) = = -0.99451580949185175491166549405037 absolute error = 4.463709643379180969586e-11 relative error = 4.4883244696326842707907646281570e-09 % glob_h = 0.01 y2(analytic)= = 0.10458634988363553498148948616483 y2(numeric) = = 0.10458634988171295965574469225211 absolute error = 1.92257532574479391272e-12 relative error = 1.8382660145266397824773683662382e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.33 y1(analytic)= = -0.99551193022825742943488570049592 y1(numeric) = = -0.99551193018355490763655925743885 absolute error = 4.470252179832644305707e-11 relative error = 4.4904054327180950051641491028894e-09 % glob_h = 0.01 y2(analytic)= = 0.094636128266160126764345149287915 y2(numeric) = = 0.094636128264682410098286926591642 absolute error = 1.477716666058222696273e-12 relative error = 1.5614720225051967276000391433655e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.34 y1(analytic)= = -0.99640850055659369166560588221229 y1(numeric) = = -0.9964085005118301826983435713919 absolute error = 4.476350896726231082039e-11 relative error = 4.4924856564609213046201762982815e-09 % glob_h = 0.01 y2(analytic)= = 0.084676443114721279878659835583843 y2(numeric) = = 0.084676443113689538261938076774859 absolute error = 1.031741616721758808984e-12 relative error = 1.2184517662414508224532661373129e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.35 y1(analytic)= = -0.99720543086521194386120630840389 y1(numeric) = = -0.99720543082039190170690463104917 absolute error = 4.482004215430167735472e-11 relative error = 4.4945645868990271868368716836017e-09 % glob_h = 0.01 y2(analytic)= = 0.074708290389534428248665758697443 y2(numeric) = = 0.074708290388949733745554464612283 absolute error = 5.84694503111294085160e-13 relative error = 7.8263670613081181040169943583294e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.36 y1(analytic)= = -0.99790264146174543057329128049666 y1(numeric) = = -0.99790264141687332455698314658871 absolute error = 4.487210601630813390795e-11 relative error = 4.4966416714338665089122307779610e-09 % glob_h = 0.01 y2(analytic)= = 0.064732666897565324311133888716703 y2(numeric) = = 0.064732666897428704456437344536865 absolute error = 1.36619854696544179838e-13 relative error = 2.1105241177956569189081669490825e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.37 y1(analytic)= = -0.99850006262571550534694151915361 y1(numeric) = = -0.99850006258079581969113164128493 absolute error = 4.491968565580987786868e-11 relative error = 4.4987163583832318352622031395008e-09 % glob_h = 0.01 y2(analytic)= = 0.054750570192850173109832832146007 y2(numeric) = = 0.05475057019316261070922720667602 absolute error = 3.12437599394374530013e-13 relative error = 5.7065633890909773645200531002444e-10 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.38 y1(analytic)= = -0.99899763461550362048515445180739 y1(numeric) = = -0.99899763457054085386169589945252 absolute error = 4.496276662345855235487e-11 relative error = 4.5007880965367770500967241338392e-09 % glob_h = 0.01 y2(analytic)= = 0.044762998476741059967283647429566 y2(numeric) = = 0.044762998477503492902123671644447 absolute error = 7.62432934840024214881e-13 relative error = 1.7032660026923483087149717827062e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.39 y1(analytic)= = -0.99939530767432543911909773848075 y1(numeric) = = -0.99939530762932410419865443514286 absolute error = 4.500133492044330333789e-11 relative error = 4.5028563347135466972860987008191e-09 % glob_h = 0.01 y2(analytic)= = 0.034770950498086647107914887365496 y2(numeric) = = 0.034770950499299968144534822673597 absolute error = 1.213321036619935308101e-12 relative error = 3.4894675562196700274451823228423e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.4 y1(analytic)= = -0.99969304203520647217794742067292 y1(numeric) = = -0.99969304199017109517708770468719 absolute error = 4.503537700085971598573e-11 relative error = 4.5049205213207528152179101851612e-09 % glob_h = 0.01 y2(analytic)= = 0.024775425453358121079773077367605 y2(numeric) = = 0.024775425455023177683310734420138 absolute error = 1.665056603537657052533e-12 relative error = 6.7205974188910295944989916995904e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.41 y1(analytic)= = -0.99989080792495874269876005981714 y1(numeric) = = -0.99989080787989386292472676338954 absolute error = 4.506487977403329642760e-11 relative error = 4.5069801039130455696611504154899e-09 % glob_h = 0.01 y2(analytic)= = 0.014777422886730378296818358805922 y2(numeric) = = 0.014777422888847972449590474224558 absolute error = 2.117594152772115418636e-12 relative error = 1.4329928628310709967898105058931e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.42 y1(analytic)= = -0.9999885855671580798132617539744 y1(numeric) = = -0.99998858552206824920646458426983 absolute error = 4.508983060679716970457e-11 relative error = 4.5090345287515273040027633679060e-09 % glob_h = 0.01 y2(analytic)= = 0.0047779425901284404999856666986414 y2(numeric) = = 0.0047779425926993285244424878329943 absolute error = 2.5708880244568211343529e-12 relative error = 5.3807428112854545718920440984843e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.43 y1(analytic)= = -0.99998636518412174468463642391346 y1(numeric) = = -0.99998636513901152735891275463887 absolute error = 4.511021732572366927459e-11 relative error = 4.5110832403617607434337062419356e-09 % glob_h = 0.01 y2(analytic)= = -0.0052220154967509045878290404963796 y2(numeric) = = -0.0052220154937260122015425736829161 absolute error = 3.0248923862864668134635e-12 relative error = 5.7925764260342202402716802215816e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=13.57 NO POLE NO POLE x[1] = = 9.44 y1(analytic)= = -0.99988414699788619063336770586951 y1(numeric) = = -0.9998841469527601624140582077818 absolute error = 4.512602821930949808771e-11 relative error = 4.5131256810900210183135115136454e-09 % glob_h = 0.01 y2(analytic)= = -0.015221451386432239660238019350561 y2(numeric) = = -0.015221451382952678422087570888845 absolute error = 3.479561238150448461716e-12 relative error = 2.2859589074744756088317449985905e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.45 y1(analytic)= = -0.99968194123018485967693666418075 y1(numeric) = = -0.99968194118504760763682251824591 absolute error = 4.513725204011414593484e-11 relative error = 4.5151612906570379121966888551485e-09 % glob_h = 0.01 y2(analytic)= = -0.025219365143659432048973937177309 y2(numeric) = = -0.025219365139724583632181094197739 absolute error = 3.934848416792842979570e-12 relative error = 1.5602487986427879340968017174697e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.46 y1(analytic)= = -0.99937976810142601770370285120988 y1(numeric) = = -0.99937976805628213969685159870649 absolute error = 4.514387800685125250339e-11 relative error = 4.5171895057084692828822927130220e-09 % glob_h = 0.01 y2(analytic)= = -0.035214756985388326060554181182105 y2(numeric) = = -0.035214756980997618460055811514848 absolute error = 4.390707600498369667257e-12 relative error = 1.2468373989689060811014647646691e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.47 y1(analytic)= = -0.99897765782867073049659952526208 y1(numeric) = = -0.99897765778352483469016691491891 absolute error = 4.514589580643261034317e-11 relative error = 4.5192097593613389310865012801188e-09 % glob_h = 0.01 y2(analytic)= = -0.045206627380764214242090580475967 y2(numeric) = = -0.04520662737591712192828672030344 absolute error = 4.847092313803860172527e-12 relative error = 1.0722083452450463434095127461413e-08 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.48 y1(analytic)= = -0.99847565062261118280735564261411 y1(numeric) = = -0.99847565057746788721139113585771 absolute error = 4.514329559596450675640e-11 relative error = 4.5212214807456622720633390483080e-09 % glob_h = 0.01 y2(analytic)= = -0.055193977151074089912432241653559 y2(numeric) = = -0.055193977145770133980197483849166 absolute error = 5.303955932234757804393e-12 relative error = 9.6096643257235203048813159778087e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.49 y1(analytic)= = -0.99787379668354964264681914241071 y1(numeric) = = -0.99787379663841357464212303393476 absolute error = 4.513606800469610847595e-11 relative error = 4.5232240945404709616809889553102e-09 % glob_h = 0.01 y2(analytic)= = -0.065175807569663685816681649783686 y2(numeric) = = -0.065175807563902434129615486115918 absolute error = 5.761251687066163667768e-12 relative error = 8.8395555067088405340941448518945e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.5 y1(analytic)= = -0.99717215619637847289160164017799 y1(numeric) = = -0.99717215615125426875568204229254 absolute error = 4.512420413591959788545e-11 relative error = 4.5252170205034330908006743634267e-09 % glob_h = 0.01 y2(analytic)= = -0.075151120461809307283482504534007 y2(numeric) = = -0.075151120455590374613374560879307 absolute error = 6.218932670107943654700e-12 relative error = 8.2752361267431982673242232236052e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.51 y1(analytic)= = -0.99637079932456169220170055576772 y1(numeric) = = -0.99637079927945399663287878130459 absolute error = 4.510769556882177446313e-11 relative error = 4.5271996729932486304341460631419e-09 % glob_h = 0.01 y2(analytic)= = -0.085118918304534472784989812856164 y2(numeric) = = -0.08511891829785752094647640589795 absolute error = 6.676951838513406958214e-12 relative error = 7.8442630281377894178667847954827e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.52 y1(analytic)= = -0.99546980620311868708799156433553 y1(numeric) = = -0.99546980615803215272770472423782 absolute error = 4.508653436028684009771e-11 relative error = 4.5291714604839804142900268255488e-09 % glob_h = 0.01 y2(analytic)= = -0.095078204326361380318646497754086 y2(numeric) = = -0.09507820431922611829903543429891 absolute error = 7.135262019611063455176e-12 relative error = 7.5046242934067917642671530731358e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.53 y1(analytic)= = -0.99446926693061077675253773398721 y1(numeric) = = -0.99446926688555006370588764205806 absolute error = 4.506071304665009192915e-11 relative error = 4.5311317850704590028451088268743e-09 % glob_h = 0.01 y2(analytic)= = -0.10502798260698722454725429037249 y2(numeric) = = -0.10502798259939340863149532633711 absolute error = 7.59381591575896403538e-12 relative error = 7.2302787574001904357325258307546e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.54 y1(analytic)= = -0.99336928156013143203855347880575 y1(numeric) = = -0.99336928151510120739315122739746 absolute error = 4.503022464540225140829e-11 relative error = 4.5330800419638751899137783910208e-09 % glob_h = 0.01 y2(analytic)= = -0.11496725817687539714868821905492 y2(numeric) = = -0.11496725816882283103946709431923 absolute error = 8.05256610922112473569e-12 relative error = 7.0042255829328145920359009251231e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.55 y1(analytic)= = -0.99216996008930104946062020501596 y1(numeric) = = -0.992169960044305986803776041668 absolute error = 4.499506265684416334796e-11 relative error = 4.5350156189766465825079821299127e-09 % glob_h = 0.01 y2(analytic)= = -0.12489503711675161133821211423883 y2(numeric) = = -0.12489503710824014627114658186764 absolute error = 8.51146506706553237119e-12 relative error = 6.8148945414932966335537526694404e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.56 y1(analytic)= = -0.99087142244926728082941296820604 y1(numeric) = = -0.99087142240431205976372136435374 absolute error = 4.495522106569160385230e-11 relative error = 4.5369378959956144879149943434353e-09 % glob_h = 0.01 y2(analytic)= = -0.13481032665699500103385605836142 y2(numeric) = = -0.13481032664802453588777283212176 absolute error = 8.97046514608322623966e-12 relative error = 6.6541379792864475039195406967881e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.57 y1(analytic)= = -0.98947379849271201842880930751569 y1(numeric) = = -0.98947379844780132408617936635426 absolute error = 4.491069434262994116143e-11 relative error = 4.5388462444425941450808065143152e-09 % glob_h = 0.01 y2(analytic)= = -0.14471213527691425563776488291664 y2(numeric) = = -0.14471213526748473704003693550382 absolute error = 9.42951859772794741282e-12 relative error = 6.5160524234433203182824924006575e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=255.5MB, alloc=4.4MB, time=13.76 x[1] = = 9.58 y1(analytic)= = -0.98797722798086623503686840020208 y1(numeric) = = -0.98797722793600475759105000156847 absolute error = 4.486147744581839863361e-11 relative error = 4.5407400267212649923455205228146e-09 % glob_h = 0.01 y2(analytic)= = -0.15459947280389886290276941436475 y2(numeric) = = -0.15459947279401028532969357024803 absolute error = 9.88857757307584411672e-12 relative error = 6.3962556881542372740408697721708e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.59 y1(analytic)= = -0.98638186056953397729585750808878 y1(numeric) = = -0.98638186052472641147351383378174 absolute error = 4.480756582234367430704e-11 relative error = 4.5426185956493480066489707286483e-09 % glob_h = 0.01 y2(analytic)= = -0.16447135051243554484251957207247 y2(numeric) = = -0.16447135050208795071471485332638 absolute error = 1.034759412780471874609e-11 relative error = 6.2914264980285095808789543258975e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.6 y1(analytic)= = -0.98468785579412691002034207988373 y1(numeric) = = -0.98468785574937795461071940314625 absolute error = 4.474895540962267673748e-11 relative error = 4.5444812938749739999563828981867e-09 % glob_h = 0.01 y2(analytic)= = -0.17432678122297998512410172652042 y2(numeric) = = -0.17432678121217346489690942736778 absolute error = 1.080652022719229915264e-11 relative error = 6.1990017548535849817732085759533e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.61 y1(analytic)= = -0.98289538305371090797643752884989 y1(numeric) = = -0.98289538300902526533968338675476 absolute error = 4.468564263675414209513e-11 relative error = 4.5463274532760999183972520584532e-09 % glob_h = 0.01 y2(analytic)= = -0.18416477940067396085279388755953 y2(numeric) = = -0.18416477938940865310166087356266 absolute error = 1.126530775113301399687e-11 relative error = 6.1169718704051986615020781267526e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.62 y1(analytic)= = -0.98100462159406629045975029811516 y1(numeric) = = -0.98100462154944866603393139529037 absolute error = 4.461762442581890282479e-11 relative error = 4.5481563943417794408754225811010e-09 % glob_h = 0.01 y2(analytic)= = -0.19398436125389800711804424947092 y2(numeric) = = -0.19398436124217409861887150031532 absolute error = 1.172390849917274915560e-11 relative error = 6.0437390021496713715627884484377e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.63 y1(analytic)= = -0.97901576048976339263443399538486 y1(numeric) = = -0.97901576044521849444130541185873 absolute error = 4.454489819312858352613e-11 relative error = 4.5499674255340392782924020538237e-09 % glob_h = 0.01 y2(analytic)= = -0.20378454483264975911634544167295 y2(numeric) = = -0.20378454482046748492078438223731 absolute error = 1.218227419556105943564e-11 relative error = 5.9780167360411383716414946723539e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.64 y1(analytic)= = -0.97692899862525526606128971734918 y1(numeric) = = -0.97692899858078780421086721225342 absolute error = 4.446746185042250509576e-11 relative error = 4.5517598426290532714086526513989e-09 % glob_h = 0.01 y2(analytic)= = -0.21356435012673813409877387614672 y2(numeric) = = -0.21356435011409777760445356899072 absolute error = 1.264035649432030715600e-11 relative error = 5.9187577359325112265470811662243e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.65 y1(analytic)= = -0.97474454467498939912910172337994 y1(numeric) = = -0.97474454463060408532308913979143 absolute error = 4.438531380601258358851e-11 relative error = 4.5535329280362423899253316061949e-09 % glob_h = 0.01 y2(analytic)= = -0.22332279916378353380682764984038 y2(numeric) = = -0.2233227991506854268224964533115 absolute error = 1.309810698433119652888e-11 relative error = 5.8651006674536294856292798908176e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.66 y1(analytic)= = -0.97246261708254044620059181388743 y1(numeric) = = -0.97246261703824199323471579818486 absolute error = 4.429845296587601570257e-11 relative error = 4.5552859500938597368879281083466e-09 % glob_h = 0.01 y2(analytic)= = -0.23305891610701426745798598140296 y2(numeric) = = -0.23305891609345879026355181121016 absolute error = 1.355547719443417019280e-11 relative error = 5.8163306604454757455363930978590e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.67 y1(analytic)= = -0.97008344403876605218268848348545 y1(numeric) = = -0.97008344399455917344799293521584 absolute error = 4.420687873469554826961e-11 relative error = 4.5570181623395453217138772312752e-09 % glob_h = 0.01 y2(analytic)= = -0.24277172735284941572018837380244 y2(numeric) = = -0.24277172733883699712164224207229 absolute error = 1.401241859854613173015e-11 relative error = 5.7718494452940126286538888242866e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.68 y1(analytic)= = -0.96760726345898795692045040320274 y1(numeric) = = -0.96760726341487736590360326856484 absolute error = 4.411059101684713463790e-11 relative error = 4.5587288027542553124256710124142e-09 % glob_h = 0.01 y2(analytic)= = -0.2524602616282583774701548371608 y2(numeric) = = -0.25246026161378949484936288162406 absolute error = 1.446888262079195553674e-11 relative error = 5.7311525098936302564236925090892e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.69 y1(analytic)= = -0.96503432295920066128518915643983 y1(numeric) = = -0.96503432291519107106785437006802 absolute error = 4.400959021733478637181e-11 relative error = 4.5604170929778843097565325846927e-09 % glob_h = 0.01 y2(analytic)= = -0.26212355008788736346200402497301 y2(numeric) = = -0.26212355007296254282135378197042 absolute error = 1.492482064065024300259e-11 relative error = 5.6938114242867923394467832825384e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.7 y1(analytic)= = -0.96236487983131003407035637089144 y1(numeric) = = -0.96236487978740615682768393663631 absolute error = 4.390387724267243425513e-11 relative error = 4.5620822374948064633491522233651e-09 % glob_h = 0.01 y2(analytic)= = -0.27176062641094312433774089682484 y2(numeric) = = -0.27176062639556294033962811521282 absolute error = 1.538018399811278161202e-11 relative error = 5.6594600186325813772617586567030e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.71 y1(analytic)= = -0.95959920101740433581387123224931 y1(numeric) = = -0.95959920097361088231215861407173 absolute error = 4.379345350171261817758e-11 relative error = 4.5637234227874614942975313925929e-09 % glob_h = 0.01 y2(analytic)= = -0.28137052689782422468754902973106 y2(numeric) = = -0.28137052688198930068869186845408 absolute error = 1.583492399885716127698e-11 relative error = 5.6277834688092234582699457334771e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.72 y1(analytic)= = -0.95673756308306023242306540492194 y1(numeric) = = -0.95673756303938191151664357381913 absolute error = 4.367832090642183110281e-11 relative error = 4.5653398164560043766525444978552e-09 % glob_h = 0.01 y2(analytic)= = -0.29095229056649020011300734215994 y2(numeric) = = -0.29095229055020120819357534217912 absolute error = 1.628899191943199998082e-11 relative error = 5.5985096002224253822418978408820e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=13.96 NO POLE NO POLE x[1] = = 9.73 y1(analytic)= = -0.95378025218968646797863795078318 y1(numeric) = = -0.953780252146127986106035602821 absolute error = 4.355848187260234796218e-11 relative error = 4.5669305663019219940742782236381e-09 % glob_h = 0.01 y2(analytic)= = -0.30050495924855896045783227226612 y2(numeric) = = -0.3005049592318166214453780436349 absolute error = 1.674233901245422863122e-11 relative error = 5.5714019010934225491214886615712e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.74 y1(analytic)= = -0.95072756406590796232729298795066 y1(numeric) = = -0.95072756402247402300673261196024 absolute error = 4.343393932056037599042e-11 relative error = 4.5684947993733959057828098118619e-09 % glob_h = 0.01 y2(analytic)= = -0.31002757768512282954590323853619 y2(numeric) = = -0.31002757766792791303408535563594 absolute error = 1.719491651181788290025e-11 relative error = 5.5462538656099071736397070244763e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.75 y1(analytic)= = -0.94757980397799319502945431997722 y1(numeric) = = -0.94757980393468849835373395126079 absolute error = 4.330469667572036871643e-11 relative error = 4.5700316209700567512674792888410e-09 % glob_h = 0.01 y2(analytic)= = -0.31951919362227363990244401392754 y2(numeric) = = -0.31951919360462696426453016615967 absolute error = 1.764667563791384776787e-11 relative error = 5.5228843807033507700627254270762e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.76 y1(analytic)= = -0.94433728669932783289901849942829 y1(numeric) = = -0.94433728665615707502983314788311 absolute error = 4.317075786918535154518e-11 relative error = 4.5715401136046320571312693305214e-09 % glob_h = 0.01 y2(analytic)= = -0.32897885790632733002849187561677 y2(numeric) = = -0.32897885788822976242563187713566 absolute error = 1.809756760285999848111e-11 relative error = 5.5011339385259394146343683438143e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.77 y1(analytic)= = -0.94100033647893765374695379161714 y1(numeric) = = -0.94100033643590552640871067900467 absolute error = 4.303212733824311261247e-11 relative error = 4.5730193359188344752754484519260e-09 % glob_h = 0.01 y2(analytic)= = -0.33840562457873852184828064999273 y2(numeric) = = -0.33840562456019097823253947029482 absolute error = 1.854754361574117969791e-11 relative error = 5.4808615072015832770498402932356e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.78 y1(analytic)= = -0.93756928700906391401013986915761 y1(numeric) = = -0.93756928696617510398332175079242 absolute error = 4.288881002681811836519e-11 relative error = 4.5744683215506708988541727498848e-09 % glob_h = 0.01 y2(analytic)= = -0.34779855097069558695088813214452 y2(numeric) = = -0.34779855095169903206302966944566 absolute error = 1.899655488785846269886e-11 relative error = 5.4619419301315757127948443043842e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.79 y1(analytic)= = -0.93404448139179440270166491645709 y1(numeric) = = -0.93404448134905359131579589734472 absolute error = 4.274081138586901911237e-11 relative error = 4.5758860779501735083809650622898e-09 % glob_h = 0.01 y2(analytic)= = -0.35715669779738674219835267420704 y2(numeric) = = -0.35715669777794218956036555548165 absolute error = 1.944455263798711872539e-11 relative error = 5.4442637525498454680375215118292e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.8 y1(analytic)= = -0.93042627210475351854937775208922 y1(numeric) = = -0.93042627206216538117564613648102 absolute error = 4.258813737373161560820e-11 relative error = 4.5772715851403605431731183265297e-09 % glob_h = 0.01 y2(analytic)= = -0.36647912925192774816925294872886 y2(numeric) = = -0.36647912923203626007161020399161 absolute error = 1.989148809764274473725e-11 relative error = 5.4277273956217008288880237533066e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.81 y1(analytic)= = -0.9267150209658548012863896067548 y1(numeric) = = -0.9267150209234240068299824431891 absolute error = 4.243079445640716356570e-11 relative error = 4.5786237944200263220567098376511e-09 % glob_h = 0.01 y2(analytic)= = -0.37576491309894181774617935021249 y2(numeric) = = -0.37576491307860450522982437403553 absolute error = 2.033731251635497617696e-11 relative error = 5.4122436149327236317814579120390e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.82 y1(analytic)= = -0.92291109909711944181102371397114 y1(numeric) = = -0.92291109905485065220322781511313 absolute error = 4.226878960779589885801e-11 relative error = 4.5799416270047354923610343497718e-09 % glob_h = 0.01 y2(analytic)= = -0.3850131207677823769342212848996 y2(numeric) = = -0.38501312074700039976727306521517 absolute error = 2.078197716694821968443e-11 relative error = 5.3977321929978342432817768832205e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.83 y1(analytic)= = -0.91901488688756438933504557750164 y1(numeric) = = -0.91901488684546225902516990545758 absolute error = 4.210213030987567204406e-11 relative error = 4.5812239726021542884521865702634e-09 % glob_h = 0.01 y2(analytic)= = -0.39422282744538935571207387513578 y2(numeric) = = -0.39422282742416392236124503801547 absolute error = 2.122543335082883712031e-11 relative error = 5.3841208253647209692041691625697e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.84 y1(analytic)= = -0.91502677395516376667853261821045 y1(numeric) = = -0.91502677391323294212570703145665 absolute error = 4.193082455282558675380e-11 relative error = 4.5824696879175902185087590590441e-09 % glob_h = 0.01 y2(analytic)= = -0.40339311216876972336405895208667 y2(numeric) = = -0.40339311214710209096078074135284 absolute error = 2.166763240327821073383e-11 relative error = 5.3713441676745853908170071591890e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.85 y1(analytic)= = -0.91094715910788739753815499845279 y1(numeric) = = -0.9109471590661325167030604560655 absolute error = 4.175488083509454238729e-11 relative error = 4.5836775950853294135376899590228e-09 % glob_h = 0.01 y2(analytic)= = -0.4125230579170930203165939905931 y2(numeric) = = -0.41252305789498449461784287274429 absolute error = 2.210852569875111784881e-11 relative error = 5.3593430171833903343241172376179e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.86 y1(analytic)= = -0.9067764503038203418436730102013 y1(numeric) = = -0.9067764502622460336802584226827 absolute error = 4.157430816341458751860e-11 relative error = 4.5848464800210560463929580810073e-09 % glob_h = 0.01 y2(analytic)= = -0.42161175170339267700267135998151 y2(numeric) = = -0.42161175168084461234649251794081 absolute error = 2.254806465617884204070e-11 relative error = 5.3480636071172869815936621129447e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=14.17 NO POLE NO POLE x[1] = = 9.87 y1(analytic)= = -0.90251506461036742721588176741229 y1(numeric) = = -0.90251506456897831116312277106144 absolute error = 4.138911605275899635085e-11 relative error = 4.5859750906903087633163718344452e-09 % glob_h = 0.01 y2(analytic)= = -0.43065828466586394969887895389956 y2(numeric) = = -0.430658284642877748954602507461 absolute error = 2.298620074427644643856e-11 relative error = 5.3374569961218357686819752154180e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.88 y1(analytic)= = -0.89816342816254685603886129769815 y1(numeric) = = -0.898163428121347541512616311157 absolute error = 4.119931452624498654115e-11 relative error = 4.5870621352875727707420071027935e-09 % glob_h = 0.01 y2(analytic)= = -0.43966175215874934361745985670674 y2(numeric) = = -0.43966175213532645813060622319773 absolute error = 2.342288548685363350901e-11 relative error = 5.3274785381823016295228134088206e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.89 y1(analytic)= = -0.89372197612037705875106959670788 y1(numeric) = = -0.89372197607937214463608859400421 absolute error = 4.100491411498100270367e-11 relative error = 4.5881062803202206712937999905083e-09 % glob_h = 0.01 y2(analytic)= = -0.44862125384280243478683944057064 y2(numeric) = = -0.44862125381894436431871082610722 absolute error = 2.385807046812861446342e-11 relative error = 5.3180874209068388019335607341649e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.9 y1(analytic)= = -0.88919115262536105463443869868911 y1(numeric) = = -0.88919115258455512877658020278484 absolute error = 4.080592585785849590427e-11 relative error = 4.5891061485910976872998439397369e-09 % glob_h = 0.01 y2(analytic)= = -0.45753589377532104441381810750536 y2(numeric) = = -0.45753589375102933707577369722786 absolute error = 2.429170733804441027750e-11 relative error = 5.3092462621026994941495773589820e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.91 y1(analytic)= = -0.88457141075607267162913194182542 y1(numeric) = = -0.88457141071547031032784380634424 absolute error = 4.060236130128813548118e-11 relative error = 4.5900603170730946201954287533407e-09 % glob_h = 0.01 y2(analytic)= = -0.46640478049974076248502085228777 y2(numeric) = = -0.46640478047501701466743384706626 absolute error = 2.472374781758700522151e-11 relative error = 5.3009207562358480578973138670035e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.92 y1(analytic)= = -0.87986321248284906651496959250613 y1(numeric) = = -0.87986321244245483401608919694424 absolute error = 4.039423249888039556189e-11 relative error = 4.5909673146685615421554281241649e-09 % glob_h = 0.01 y2(analytic)= = -0.47522702713477986132990452209273 y2(numeric) = = -0.47522702710962571762579974932102 absolute error = 2.515414370410477277171e-11 relative error = 5.2930793637228818101716481904085e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.93 y1(analytic)= = -0.87506702862159407616974857863779 y1(numeric) = = -0.87506702858141252415867811394171 absolute error = 4.018155201107046469608e-11 relative error = 4.5918256198458832407376627522165e-09 % glob_h = 0.01 y2(analytic)= = -0.48400175146312668472825365246634 y2(numeric) = = -0.48400175143754383785162505965734 absolute error = 2.558284687662859280900e-11 relative error = 5.2856930371206731194802815707750e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.94 y1(analytic)= = -0.87018333878669701953083342106317 y1(numeric) = = -0.87018333874673268662614598797505 absolute error = 3.996433290468743308812e-11 relative error = 4.5926336581449599051646878767167e-09 % glob_h = 0.01 y2(analytic)= = -0.49272807601966064389716004128963 y2(numeric) = = -0.49272807599365083459596796318107 absolute error = 2.600980930119207810856e-11 relative error = 5.2787349792006260309032075012776e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.95 y1(analytic)= = -0.86521263134307165834058800307683 y1(numeric) = = -0.86521263130332906958812028508819 absolute error = 3.974258875246771798864e-11 relative error = 4.5933897995427091065319198811265e-09 % glob_h = 0.01 y2(analytic)= = -0.5014051281791979983314046143732 y2(numeric) = = -0.50140512815276301529525328708754 absolute error = 2.643498303615132728566e-11 relative error = 5.2721804286580183298573611053633e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.96 y1(analytic)= = -0.86015540335732011273960623537296 y1(numeric) = = -0.86015540331780377910709354147985 absolute error = 3.951633363251269389311e-11 relative error = 4.5940923556690229740348227794080e-09 % glob_h = 0.01 y2(analytic)= = -0.51003204024375364699227878479226 y2(numeric) = = -0.5100320402168953267547751642045 absolute error = 2.685832023750362058776e-11 relative error = 5.2660064698420785028859320683074e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.97 y1(analytic)= = -0.85501216054802661527548569200894 y1(numeric) = = -0.85501216050874103314779519171347 absolute error = 3.928558212769050029547e-11 relative error = 4.5947395768628722791106535534754e-09 % glob_h = 0.01 y2(analytic)= = -0.51860794952931020373844434075647 y2(numeric) = = -0.51860794950203043057423986654561 absolute error = 2.727977316420447421086e-11 relative error = 5.2601918634227764105374000553105e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.98 y1(analytic)= = -0.84978341723518607391032160643442 y1(numeric) = = -0.84978341719613572458533960057881 absolute error = 3.905034932498200585561e-11 relative error = 4.5953296490574410056715479895288e-09 % glob_h = 0.01 y2(analytic)= = -0.52713199845208568016359609786023 y2(numeric) = = -0.52713199842438638598011362968996 absolute error = 2.769929418348246817027e-11 relative error = 5.2547168953546708339330286973491e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 9.99 y1(analytic)= = -0.84446969628877250112847775450166 y1(numeric) = = -0.84446969624996185031370684054125 absolute error = 3.881065081477091396041e-11 relative error = 4.5958606904822943576797989688892e-09 % glob_h = 0.01 y2(analytic)= = -0.53560333461429114914453304551418 y2(numeric) = = -0.53560333458617431336838178334262 absolute error = 2.811683577615126217156e-11 relative error = 5.2495632418717654599209289500047e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = = 10 y1(analytic)= = -0.83907152907645245225886394782406 y1(numeric) = = -0.8390715290378859495687859470352 absolute error = 3.856650269007800078886e-11 relative error = 4.5963307481696227614411327559137e-09 % glob_h = 0.01 y2(analytic)= = -0.54402111088936981340474766185138 y2(numeric) = = -0.54402111086083746286282944844423 absolute error = 2.853235054191821340715e-11 relative error = 5.2447138485624779594631778003806e-09 % glob_h = 0.01 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=267.0MB, alloc=4.4MB, time=14.37 x[1] = = 10.01 y1(analytic)= = -0.83358945541044870162431592024222 y1(numeric) = = -0.8335894553721307800785764371111 absolute error = 3.831792154573948313112e-11 relative error = 4.5967377942505561730677571540382e-09 % glob_h = 0.01 y2(analytic)= = -0.55238448550670895525770935853808 y2(numeric) = = -0.55238448547776316405302034879046 absolute error = 2.894579120468900974762e-11 relative error = 5.2401528218405131581790462101725e-09 % glob_h = 0.01 Finished! Iterations = 991 Total Elapsed Time = 14 Seconds Elapsed Time(since restart) = 14 Seconds Time to Timeout = 14 Minutes 45 Seconds Percent Done = 100.2 % > quit memory used=267.2MB, alloc=4.4MB, time=14.38