ABSTRACT
During the past three decades, research on and application of the group properties of differential equations has generated a substantial literature. Because of the versatility of Lie's ideas, it is not surprising that group analysis would also find applications in numerical analysis. The passage from a partial differential equation to a difference scheme inhibits a group analysis because the difference operators do not usually have the same group properties as the differential operators. A related approach to that of Janenko and Shokin has been introduced by Postell [1990] and Ames, Postell, and Adams [1993], In addition to classical optimal finite-difference schemes, they introduce invariant algorithms in which the terms added to a basic finite-difference scheme are selected to make the method high order and also to preserve some or all of the original equation's symmetry group. Examples include both hyperbolic and parabolic partial differential equations.
