# Numerics for heat equation

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)?

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The way the equation is written looks unusual. Also don't you need to specify the conditions at the boundary of the spatial domain? – Dmitri Chubarov Jan 23 at 18:16
That's not the heat equation. Maybe you inserted an extra time derivative by mistake. – David Ketcheson Jan 24 at 11:22
What is $\Tr$ in this case? – Martin Jan 26 at 15:03