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- Title
Analytical and numerical stability of partial differential equations with piecewise constant arguments.
- Authors
Wang, Qi; Wen, Jiechang
- Abstract
This article is concerned with the stability analysis of the analytic and numerical solutions of a partial differential equation with piecewise constant arguments of mixed type. First, by means of the similar technique in Wiener and Debnath [Int J Math Math Sci 15 (1992), 781-788], the sufficient conditions under which the analytic solutions asymptotically stable are obtained. Then, the θ-methods are used to solve the above-mentioned equation, the sufficient conditions for the asymptotic stability of numerical methods are derived. Finally, some numerical experiments are given to demonstrate the conclusions.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1-16, 2014
- Subjects
ASYMPTOTIC theory in partial differential equations; PIECEWISE constant approximation; NUMERICAL solutions to difference equations; ASYMPTOTIC efficiencies; NUMERICAL solutions to equations
- Publication
Numerical Methods for Partial Differential Equations, 2014, Vol 30, Issue 1, p1
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.21789