ABSTRACT
The aim of this section is to develop the entire set of invariant difference schemes for the heat equation with a source,
ut = (K(u)ux)x +Q(u), (4.1)
for all special cases of the coefficients K(u) and Q(u) in which the symmetry group admitted by Eq. (4.1) is extended. This set of invariant difference models corresponds to the Lie group classification [28] (see also [58,74]) of Eq. (4.1) with arbitrary K(u) and Q(u). This classification contains the result due to Ovsyannikov [112] for Eq. (4.1) with Q ≡ 0 as well as the symmetries for the linear case (K ≡ 1, Q ≡ 0), which were already known to S. Lie.
