Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations

Abstract

In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc.