I want to simulate on my computer the solution of the heat equation in 3 space dimensions with Cauchy initial data, that is $$\partial_t u=Tr[A(x)\cdot \Delta u], u(0,x)=u_0(x) $$
where $u_0\in C(\mathbb{R}^3,\mathbb{R})$.
Even if $A$ is constant I'm not sure what's numerically the best way to do this but I'm sure this must be in standard toolboxes of Matlab, Scilab etc. however I have quite some trouble with the documentation.
Could someone give me pointers in the right direction? More general, what is a good book or lecture notes that deal with numerics for parabolic PDEs (with multidimensions in space)?
