Thomas Decomposition for Differential Systems and for Difference Systems

Given a system of linear or nonlinear partial differential equations, various tasks like determining all power series solutions, finding all compatibility conditions, or deciding whether another given equation is a consequence of the system, require formal manipulation of the system. The Thomas decomposition method lends itself to answering such questions. It splits a differential system into finitely many so-called simple differential systems whose solution sets form a partition of the original solution set. This talk gives an introduction to this method and presents recent advances in a similar technique for difference equations and applications to the study of finite difference schemes.