A finite differences method for a two-dimensional nonlinear hyperbolic equation in a class of discontinuous functions


RASULOV M., Coskun E. , SINSOYSAL B.

APPLIED MATHEMATICS AND COMPUTATION, vol.140, pp.279-295, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 140
  • Publication Date: 2003
  • Doi Number: 10.1016/s0096-3003(02)00225-4
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.279-295

Abstract

A numerical scheme is proposed for a scalar two-dimensional nonlinear first-order wave equation with both continuous and piecewise continuous initial conditions. It is typical of such problems to assume formal solutions with discontinuities at unknown locations, which justifies the search for a scheme that does not rely on the regularity of the solution. To this end, an auxiliary problem which is equivalent to, but has more advantages then, the original system is formulated and shown that regularity of the solution of the auxiliary problem is higher than that of the original system. An efficient numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments of physical interest are presented. (C) 2002 Elsevier Science Inc. All rights reserved.