A heat transfer with a source: the complete set of invariant difference schemes

In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where a few invariant models for heat transfer equations were presented.