Abstract. The present paper studies the application of symbolic facilities of Computer Algebra Systems (CAS), in particular Maple, to the development of numerical methods. As will be shown the complex algebraic relationships in the derivation of a particular numerical method can be captured by computer algebra. We use the formalism of term rewriting system in order to demonstrate the derivation of numerical schemes with the given properties, such as conservativity or non-linear stability property (TVD schemes) using CAS Maple. In order to demonstrate our approach we consider a two-dimensional inviscid gas flow involving shock waves.