how to solve 2d heat equation?

I am trying to solve a pde (steady state 2d heat equation). The system has certain number of nodes in x and y directions and the temperature of the boundary nodes is given. The temperature of all other nodes is the average value of the surrounding 4 nodes. How do I carry out iterations so the the error comes out to be nearly zero when we calculate successive nodal temperatures?

Answer 1

[John D'Errico]

Why iterate at all? Form a sparse linear system, and solve using backslash.

As it turns out, if the domain is a rectangular one, you can just use my inpaint_nans tool from the file exchange, as it does exactly what you want.