给出如下差分格式正确Matlab代码： 1iA*B(u(i,j,k+1)-u(i,j,k))/2 + B*(u(i+1,j,k+1)-2*u(i,j,k+1)+u(i-1,j,k+1)+u(i+1,j,k)-2*u(i,j,k)+u(i-1,j,k))/(2*hx^2) + A*(u(i,j+1,k+1)-2*u(i,j,k+1)+u(i,j-1,k+1)+u(i,j+1,k)-2*u(i,j,k)+u(i,j-1,k))/(2*hy^2) +AB(((1/2)*(|u(i,j,k+1)|^2+|u(i,j,k)|^2) +(1/3)*(|u(i,j,k+1)|^4+|u(i,j,k+1)|^2*|u(i,j,k)|^2+|u(i,j,k)|^4))*(1/2)*(u(i,j,k+1)+u(i,j,k)) = 0; 差分格式的边界条件为u(0,y,t)=u(m,y,t)=u(x,0,t)=u(x,n,t)=0， 初始条件u(x,y,0)=exp(-(x^2+y^2)/2)。 差分格式中的A、B分别为x,y 方向上的紧致差分格式算子， 满足A与u(i,j,k)作用得到:(1/12)*(u(i+1,j,k)+10*u(i,j,k)+u(i-1,j,k)) A与u(i,j,k)作用得到:u(i,j,k),i=0,m; B与u(i,j,k)作用得到:(1/12)*(u(i,j+1,k)+10*u(i,j,k)+u(i,j-1,k)) B与u(i,j,k)作用得到:u(i,j,k),j=0,n; AB算子与u(I,j,k)作用得到 (1/144)*(u(i+1,j+1,k)+10*u(i+1,j,k)+u(i+1,j-1,k)+10*u(i,j+1,k)+10*u(i,j,k) +10*u(i,j-1,k)+u(i-1,j+1,k)+u(i-1,j,k)+u(i-1,j-1,k)) 空间区域[-2*pi,2*pi]*[-2*pi,2*pi],空间步长hx=hy=4*pi/64;时间步长t=0.01 用牛顿迭代法求解上面的非线性方程组，并画出数值解图形，输出误差值

以下是可能的差分格式正确的Matlab代码，供参考：

% 初始化参数
m = 64; n = 64;
hx = 4*pi/m; hy = 4*pi/n;
x = linspace(-2*pi, 2*pi, m+1); x = x(1:end-1);
y = linspace(-2*pi, 2*pi, n+1); y = y(1:end-1);
[X, Y] = meshgrid(x, y);
T = 2;
dt = 0.01;
Nt = T/dt;
t = linspace(0, T, Nt+1);
u = zeros(m, n, Nt+1);
u(:, :, 1) = exp(-(X.^2 + Y.^2)/2);

% 紧致差分格式算子
A = 1/12 * [-1 10 -1];
B = 1/12 * [-1; 10; -1];

% 求解非线性方程组
for k = 1:Nt
    F = @(uk) G(u(:, :, k), uk, hx, hy, dt, A, B);
    J = @(uk) DG(u(:, :, k), uk, hx, hy, dt, A, B);
    uk = u(:, :, k+1);
    err = 1;
    tol = 1e-6;
    max_iter = 100;
    iter = 1;
    while err > tol && iter <= max_iter
        Jk = J(uk);
        Fk = F(uk);
        delta = Jk\-Fk(:);
        delta = reshape(delta, m, n);
        uk = uk + delta;
        err = norm(delta(:))/norm(uk(:));
        iter = iter + 1;
    end
    u(:, :, k+1) = uk;
end

% 绘制数值解图形
[Xt, Yt] = meshgrid(x, y);
for k = 1:Nt+1
    surf(Xt, Yt, u(:, :, k));
    axis([-2*pi 2*pi -2*pi 2*pi -1 2]);
    shading interp;
    drawnow;
end

% 输出误差值
u_exact = zeros(m, n, Nt+1);
for k = 1:Nt+1
    u_exact(:, :, k) = exp(-(X.^2 + Y.^2)/2).*exp(1i*k*dt);
end
err = norm(u(:) - u_exact(:))/norm(u_exact(:));
disp(['误差值为：', num2str(err)]);

% 定义非线性方程组
function Fk = G(u, uk, hx, hy, dt, A, B)
    m = size(u, 1);
    n = size(u, 2);
    Fk = zeros(m, n);
    for i = 2:m-1
        for j = 2:n-1
            Fk(i, j) = 1i*A*B*(uk(i, j) - u(i, j))/2 ...
                + B*(uk(i+1, j) - 2*uk(i, j) + uk(i-1, j) ...
                + u(i+1, j) - 2*u(i, j) + u(i-1, j))/(2*hx^2) ...
                + A*(uk(i, j+1) - 2*uk(i, j) + uk(i, j-1) ...
                + u(i, j+1) - 2*u(i, j) + u(i, j-1))/(2*hy^2) ...
                + AB(u, uk, i, j)*(1/2)*(uk(i, j) + u(i, j));
        end
    end
end

% 定义非线性方程组的雅可比矩阵
function Jk = DG(u, uk, hx, hy, dt, A, B)
    m = size(u, 1);
    n = size(u, 2);
    Jk = zeros(m*n, m*n);
    for i = 2:m-1
        for j = 2:n-1
            idx = i + (j-1)*m;
            Jk(idx, idx) = 1 - AB(u, uk, i, j)*(1/2);
            Jk(idx, idx-1) = A/2/hy^2;
            Jk(idx, idx+1) = A/2/hy^2;
            Jk(idx, idx-m) = B/2/hx^2;
            Jk(idx, idx+m) = B/2/hx^2;
            Jk(idx, idx-m-1) = AB(u, uk, i-1, j)/4/hx^2;
            Jk(idx, idx-m+1) = AB(u, uk, i+1, j)/4/hx^2;
            Jk(idx, idx+m-1) = AB(u, uk, i-1, j)/4/hx^2;
            Jk(idx, idx+m+1) = AB(u, uk, i+1, j)/4/hx^2;
        end
    end
    Jk = speye(m*n) - dt*Jk;
end

% 定义AB算子
function res = AB(u, uk, i, j)
    res = (1/144)*(uk(i+1, j+1) + 10*uk(i+1, j) + uk(i+1, j-1) ...
        + 10*uk(i, j+1) + 10*uk(i, j) + 10*uk(i, j-1) ...
        + uk(i-1, j+1) + uk(i-1, j) + uk(i-1, j-1));
    res = res - (1/144)*(u(i+1, j+1) + 10*u(i+1, j) + u(i+1, j-1) ...
        + 10*u(i, j+1) + 10*u(i, j) + 10*u(i, j-1) ...
        + u(i-1, j+1) + u(i-1, j) + u(i-1, j-1));
end