Fast solution of implicit methods for linear hyperbolic equations

Abstract

A factorisation method is described for the fast numerical solution of constant tridiagonal Toeplitz linear systems which occur repeatedly in the solution of the implicit finite difference equations derived from linear first order hyperbolic equations, i.e. the Transport equation, under a variety of boundary conditions. In this paper, we show that such special linear systems can be solved efficiently by the factorisation of the coefficient matrix into two easily inverted matrices.