Speed up nested for loop

Hi,

I am looking for ways to speed up the nested for loop below, but am having trouble working out how- I have tried to vectorise with meshgrid but this didn't seem to work greatly.

for ix=2:nx-1
    for jy=2:ny-1    
        phinew(ix,jy)=0.5*1/((dx^2)+(dy^2))*((dy^2)*(phiold(ix+1,jy)+phiold(ix-1,jy))+(dx^2)*(phiold(ix,jy+1)+phiold(ix,jy-1)));  
    end
end

nx and ny are both = 100, and phinew and phiold are 100x100 doubles. Dy and Dx are related to lengths input by the user.

[dpb]

But dx, dy are independent of ix,jy. Compute the constants outside the loop; not sure if the ML JIT compiler is smart enough to find the invariant common expressions or not. Don't rely on it; give it some help.

Look at filter2

Reverse order of the loops and iterate down column first...altho 100x100 is small enough to not make cache miss likely.