Numerical solution of first-order hyperbolic partial differential-difference equation with shift

✍ Scribed by Paramjeet Singh; Kapil K. Sharma

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 167 KB
• Volume: 26
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20419

✦ Synopsis

Abstract

In this article, we continue the numerical study of hyperbolic partial differential‐difference equation that was initiated in (Sharma and Singh, Appl Math Comput 201(2008), 229–238). In Sharma and Singh, the authors consider the problem with sufficiently small shift arguments. The term negative shift and positive shift are used for delay and advance arguments, respectively. Here, we propose a numerical scheme that works nicely irrespective of the size of shift arguments. In this article, we consider hyperbolic partial differential‐difference equation with negative or positive shift and present a numerical scheme based on the finite difference method for solving such type of initial and boundary value problems. The proposed numerical scheme is analyzed for stability and convergence in L^∞^ norm. Finally, some test examples are given to validate convergence, the computational efficiency of the numerical scheme and the effect of shift arguments on the solution.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010