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Copy pathglobal_trunc_error.m
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135 lines (103 loc) · 5.59 KB
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function global_trunc_error(rate_func_in, X, t_0, t_f)
h_values = logspace(-4, -1, 50);
g_e_e_fw = zeros(size(h_values));
g_e_ex_m = zeros(size(h_values));
g_e_e_bw = zeros(size(h_values));
g_e_im_m = zeros(size(h_values));
X_0 = X(t_0);
X_f = X(t_f);
num_evals_fw_list=zeros(size(h_values));
num_evals_ex_list=zeros(size(h_values));
num_evals_bw_list=zeros(size(h_values));
num_evals_im_list=zeros(size(h_values));
for i = 1:length(h_values)
h = h_values(i);
t_current = t_0;
x_current_fw_e = X_0;
x_current_ex_mid = X_0;
x_current_bw_e = X_0;
x_current_im_mid = X_0;
num_evals_fw_sum=0;
num_evals_ex_sum=0;
num_evals_bw_sum=0;
num_evals_im_sum=0;
while t_current < t_f
if t_current + h > t_f
h_step = t_f - t_current;
else
h_step = h;
end
[x_current_fw_e,num_evals_fw] = forward_euler_step(rate_func_in, t_current, x_current_fw_e, h_step);
[x_current_ex_mid,num_evals_ex] = explicit_midpoint_step(rate_func_in, t_current, x_current_ex_mid, h_step);
[x_current_bw_e,num_evals_bw] = backward_euler_step(rate_func_in,t_current,x_current_bw_e, h_step);
[x_current_im_mid,num_evals_im] = implicit_midpoint_step(rate_func_in, t_current, x_current_im_mid, h_step);
num_evals_fw_sum=num_evals_fw_sum+num_evals_fw;
num_evals_ex_sum=num_evals_ex_sum+num_evals_ex;
num_evals_bw_sum=num_evals_bw_sum+num_evals_bw;
num_evals_im_sum=num_evals_im_sum+num_evals_im;
t_current = t_current + h_step;
end
g_e_e_fw(i) = abs(x_current_fw_e - X_f);
g_e_ex_m(i) = abs(x_current_ex_mid - X_f);
g_e_e_bw(i) = abs(x_current_bw_e - X_f);
g_e_im_m(i) = abs(x_current_im_mid - X_f);
num_evals_fw_list(i)=num_evals_fw_sum;
num_evals_ex_list(i)=num_evals_ex_sum;
num_evals_bw_list(i)=num_evals_bw_sum;
num_evals_im_list(i)=num_evals_im_sum;
end
hh = logspace(log10(min(h_values)), log10(max(h_values)), 200);
[pfw_glob,kfw_glob] =loglog_fit(h_values, g_e_e_fw)
[pex_glob,kex_glob] =loglog_fit(h_values, g_e_ex_m)
[pbw_glob,kbw_glob] =loglog_fit(h_values, g_e_e_bw)
[pim_glob,kim_glob] =loglog_fit(h_values, g_e_im_m)
figure()
loglog(h_values,g_e_e_fw,'o', 'MarkerSize',5, 'Color',[1 0 0], 'DisplayName','Forward Euler Error');
hold on
loglog(h_values,g_e_ex_m,'o', 'MarkerSize',5, 'Color',[0 1 0], 'DisplayName','Explicit Midpoint Error');
loglog(hh, kfw_glob .*hh.^pfw_glob, 'Color','r', 'LineWidth',1.5, 'DisplayName', sprintf('Forward Euler fit: p=%.2f', pfw_glob));
loglog(hh, kex_glob .*hh.^pex_glob, 'Color','g', 'LineWidth',1.5, 'DisplayName', sprintf('Explicit Midpoint fit: p=%.2f', pex_glob));
xlabel('step size h');
ylabel('global error at t_{0}{+}h');
title(sprintf('Global Truncation Error (explicit with fit lines) vs. h (t_{f} = %.3g)', t_f));
legend('Location','best');
hold off
figure()
loglog(h_values,g_e_e_fw,'o','Color','r','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Forward Euler Error');
hold on
loglog(h_values,g_e_ex_m,'o', 'Color','g','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Explicit Midpoint Error');
loglog(h_values,g_e_e_bw,'o', 'Color','b','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Backward Euler Error');
loglog(h_values,g_e_im_m,'o', 'Color','y','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Implicit Midpoint Error');
xlabel('step size h');
ylabel('global error at t_{0}{+}h');
title(sprintf('Global Truncation Error (explicit & implicit) vs. h (t_{f} = %.3g)', t_f));
legend('Location','best');
hold off
disp("with num_evals")
[pfw_glob,kfw_glob] =loglog_fit(num_evals_fw_list, g_e_e_fw)
[pex_glob,kex_glob] =loglog_fit(num_evals_ex_list, g_e_ex_m)
[pbw_glob,kbw_glob] =loglog_fit(num_evals_bw_list, g_e_e_bw)
[pim_glob,kim_glob] =loglog_fit(num_evals_im_list, g_e_im_m)
figure()
loglog(num_evals_fw_list,g_e_e_fw,'o', 'MarkerSize',5, 'Color',[1 0 0], 'DisplayName','Forward Euler Error');
hold on
loglog(num_evals_ex_list,g_e_ex_m,'o', 'MarkerSize',5, 'Color',[0 1 0], 'DisplayName','Explicit Midpoint Error');
loglog(hh, kfw_glob .*hh.^pfw_glob, 'Color','r', 'LineWidth',1.5, 'DisplayName', sprintf('Forward Euler fit: p=%.2f', pfw_glob));
loglog(hh, kex_glob .*hh.^pex_glob, 'Color','g', 'LineWidth',1.5, 'DisplayName', sprintf('Explicit Midpoint fit: p=%.2f', pex_glob));
xlabel('step size h');
ylabel('global error at t_{0}{+}h');
title(sprintf('Global Truncation Error (explicit with fit lines) vs. number of function calls (t_{f} = %.3g)', t_f));
legend('Location','best');
hold off
figure()
loglog(num_evals_fw_list,g_e_e_fw,'o','Color','r','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Forward Euler Error');
hold on
loglog(num_evals_ex_list,g_e_ex_m,'o', 'Color','g','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Explicit Midpoint Error');
loglog(num_evals_bw_list,g_e_e_bw,'o', 'Color','b','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Backward Euler Error');
loglog(num_evals_im_list,g_e_im_m,'o', 'Color','y','MarkerSize',5, 'LineWidth',0.5, 'DisplayName','Implicit Midpoint Error');
xlabel('number of function calls');
ylabel('global error at t_{0}{+}h');
title(sprintf('Global Truncation Error (explicit & implicit) vs. number of error calls (t_{f} = %.3g)', t_f));
legend('Location','best');
hold off
end