Solution of quasilinear hyperbolic initial-boundary-value problems by the method of pseudolinear equations

Abstract

A method, called the method of pseudolinear equations, for solving a class of quasilinear hyperbolic initial-boundary-value problems of second order in one space dimension is investigated. The finite-difference implementation of the method is improved vs. a previous version by elimination of iteration. The results of a series of numerical experiments show the improved finite-difference implementation to be between 1.8 and 13.9 times faster than solution of nonlinear systems of finite-difference approximations of the quasilinear hyperbolic problems by Newton's method. However, in cases with large nonlinearities, the method of pseudolinear equations shows instability, while Newton's method converges after a large amount of computing time.