Fourth‐order approximation for the three space dimensional certain mildly quasi‐linear hyperbolic equation

Abstract

AbstractIn 1995, Mohanty et al. [1] proposed a fourth‐order finite difference scheme for the numerical solution of a three space dimensional singular hyperbolic equation and discussed an operator splitting method for a linear equation having first‐order space derivative terms. In this article, we extend our strategy for the difference solution of a three space dimensional quasi‐linear hyperbolic equation. Fourth‐order approximation at the first‐time level for a more general case is also proposed. Linear stability analysis and an operator splitting technique for a linear hyperbolic equation having a first‐order time derivative term are discussed. Numerical results are given to illustrate the accuracy of the proposed methods. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 277–289, 2001