MATLAB数值解与解析解比较：四阶常微分方程组

A = [-5,2,0,0;0,-4,0,0;-3,2,-4,-1;-3,2,0,-4]; X0 = [1;2;0;1]; % 初始条件 [t, X] = ode45(@(t, X) AX, tspan, X0); % 绘制数值解 figure; plot(t, X(:, 1), 'r', t, X(:, 2), 'b', t, X(:, 3), 'g', t, X(:, 4), 'y'); xlabel('时间'); ylabel('解'); legend('X1', 'X2', 'X3', 'X4'); title('数值解'); x_analytical = expm(At') * X0; % 绘制解析解 figure; plot(t,x_analytical(:, 1), 'r', t, x_analytical(:, 2), 'b', t, x_analytical(:, 3), 'g', t, x_analytical(:, 4), 'y'); xlabel('时间'); ylabel('解'); legend('X1', 'X2', 'X3', 'X4'); title('解析解');