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 o 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, Nr. 23 (1997), 8139-8155], where a few invariant models or heat transfer equations were presented.