How can solve Laplacian of a function with coefficients?

Hi guys, I need to solve the gross pitaevskii equation using matlab, and I need to solve something like that:

where A and B are scalars, x and y are two matrix (m x m) created by meshgrid of two vectors of the same length (m), and \phi is another matrix of size m x m. I know that using del2 it's possible to compute.

.

If I use diff(\phi,2,1) and diff(\phi,2,2) to calculate by separated and respectivley, I get a matrix (m-2, m) and (m, m-2). After, I need to plot in 2D using pcolor. the problem is the size of the matrix x and Y are different from the size of psi, using diff. Also, using del2 I cant incorporate the coefficient A and B.

how can I resolve this, please! Thanks!

I will put and example of my problem below.

x = [1:10];
y = [1:10];
[X,Y] = meshgrid(x,y);
A = 2;
B = 4;
%Example of function, but in my problem, phi is a matrix generated by a N iterations of a loop,
%in others words phi is a random matrix with size length(x) times length(y).
phi = exp(X+Y);

%using diff to calculate phi
psi_1 = A*diff(phi,2,1) +B*diff(phi,2,2);

%using del2
psi_2 = 4*del2(phi,x,y); % the problem here is that I don't know how to introduce the coefficients A and B into the laplacian!

figure(1)
subplot(1,2,1)
pcolor(X,Y,psi_1); shading interp
subplot(1,2,2)
pcolor(X,Y,psi_2); shading interp

Any help I will appreciate it.

Thanks!!!!