Discretization of quasilinear evolution equations by computer algebra methods

Abstract

An algorithmic approach to construction of finite difference schemes on regular grids developed by the first two authors is applied to quasilinear evolution equations in one spatial variable. The approach combines the finite volumes method, numerical integration, and difference elimination, which is done by means of computer algebra. As a concrete example, a difference scheme for the Korteweg-de Vries equation is constructed. This scheme is strongly consistent and absolutely stable. The numerical behavior of the scheme obtained is illustrated by solving a Cauchy problem.