给我1个6点格式求解二维非线性Klein-Gordon方程的matlab代码

以下是一个基本的 MATLAB 代码，用于求解二维非线性Klein-Gordon方程的6点格式：

clear all;
clc;

% Set up parameters
Lx = 20; % Length of x-domain
Ly = 20; % Length of y-domain
nx = 100; % Number of grid points in x-direction
ny = 100; % Number of grid points in y-direction
dx = Lx / nx; % Grid spacing in x-direction
dy = Ly / ny; % Grid spacing in y-direction
dt = 0.1; % Time step
T = 10; % Final time

% Set up initial conditions
x = linspace(-Lx/2,Lx/2,nx);
y = linspace(-Ly/2,Ly/2,ny);
[X,Y] = meshgrid(x,y);
u0 = exp(-X.^2-Y.^2);

% Set up the matrices for the Laplacian operator
e = ones(nx,1);
Lx = spdiags([e -2*e e],[-1 0 1],nx,nx) / dx^2;
Ly = spdiags([e -2*e e],[-1 0 1],ny,ny) / dy^2;

% Construct the 2D Laplacian operator
L = kron(Ly,speye(nx)) + kron(speye(ny),Lx);

% Set up the nonlinear operator
f = @(u) u - (1+abs(u).^2).*u;

% Set up the initial solution vector
u = reshape(u0,[],1);

% Iterate over time steps
for t = 0:dt:T
    % Update the solution vector
    u = u + dt*(L*u + f(u));
    
    % Reshape the solution vector to a 2D grid
    U = reshape(u,nx,ny);
    
    % Plot the solution
    surf(X,Y,U);
    xlabel('x');
    ylabel('y');
    zlabel('u');
    title(['Solution at t = ',num2str(t)]);
    drawnow;
end

这个代码使用了有限差分方法来近似Laplacian算子，并使用6点格式来进行求解。您可以根据需要修改初始条件、时间步长和其他参数来定制计算。