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

Abstract

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, Nr. 23 (1997), 8139–8155], where a few invariant models for heat transfer equations were presented. © 2003 Taylor & Francis Group, LLC.