The numerical solution of hyperbolic systems using bicharacteristics

Abstract

This paper is concerned with deriving methods for solving numerically a firstorder quasilinear hyperbolic system. The basic principle of the method is to integrate along one of the bicharacteristics of the system to obtain an equivalent integral system. The numerical methods are then obtained by making suitable approximations to this integral system. Stability and convergence properties are analyzed in some detail. The methods are relatively easy to implement and have been successfully applied to problems in one, two and three space dimensions in such areas as magnetohydrodynamics and dynamic elasticity.