Using the forward time centered space scheme, I transformed the equation:

$u_t-2u_{xx}-u_{yy}=0$

to

$u_{i,j}^{n+1}=(1-2s_{x}-2s_{y})u_{i,j}^{n}+s_{x}(u_{i+1,j}^{n}+u_{i-1,j}^{n})+s_{y}(u_{i,j+1}^{n}+u_{i,j-1}^{n})$

letting $s_x=2 \Delta t/(\Delta x)^2$ and $s_y= \Delta t/(\Delta y)^2$

I think that to be stable, $s_x + s_y$ has to be less than 1/2, but I'm not sure. Can anyone help?