Dispersion and Gibbs phenomenon associated with difference approximations to initial boundary-value problems for hyperbolic equations

• Published in: Journal of computational physics Vol. 18; no. 3; pp. 233 - 247
• Main Author: Chin, Raymond C.Y.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.1975
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/0021-9991(75)90001-7

In this paper, we analyze the problem of the semidiscretized approximation for the initial boundary-value problem of the wave equation. Point-wise convergence properties for the propagation of discontinuities are investigated via a uniformly valid asymptotic expansion. An approximate error analysis using matched asymptotic expansions is constructed and compared with the asymptotic expansion of the exact solution.