有限差分法求解常微分方程组的通用matlab参考代码

以下是使用有限差分法求解常微分方程组的通用MATLAB参考代码：

function [t, y] = fdm_ode_system(f, tspan, y0, N)
% FDM_ODE_SYSTEM Solve a system of ordinary differential equations using the Finite Difference Method (FDM).
% Usage: [t, y] = fdm_ode_system(f, tspan, y0, N)
% Inputs:
% - f: function handle that defines the system of ODEs as f(t, y), where t is the independent variable and y is the vector of dependent variables
% - tspan: vector of length 2 that defines the time interval [t0, tf]
% - y0: column vector of initial values for the dependent variables
% - N: number of time steps
% Outputs:
% - t: column vector of time values
% - y: matrix of size (length(y0) x N+1) that contains the solution at each time step

% Define the time step
dt = (tspan(2) - tspan(1)) / N;

% Define the vector of time values
t = tspan(1) + (0:N)' * dt;

% Initialize the matrix of solution values
y = zeros(length(y0), N+1);

% Set the initial values
y(:,1) = y0;

% Loop over all time steps
for i = 1:N
% Calculate the derivative at the current time
dydt = f(t(i), y(:,i));

% Calculate the solution at the next time step using the Forward Euler method
y(:,i+1) = y(:,i) + dt * dydt;
end

end

% Example usage:
% Define the system of ODEs as f(t, y) = [y(2); -y(1)]
% f = @(t, y) [y(2); -y(1)];
% Define the time interval [t0, tf]
% tspan = [0, 10];
% Define the initial values for the dependent variables
% y0 = [1; 0];
% Choose the number of time steps
% N = 1000;
% Solve the system using the FDM
% [t, y] = fdm_ode_system(f, tspan, y0, N);
% Plot the solution
% plot(t, y(1,:), '-b', t, y(2,:), '-r')