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

In 1995, Mohanty ct 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. (C) 2001 John Wiley & Sons, Inc.