Analytical and Numerical Stability of Partial Differential Equations with Piecewise Constant Arguments

摘要

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 abovementioned equation, the sufficient conditions for the asymptotic stability of numerical methods are derived. Finally, some numerical experiments are given to demonstrate the conclusions.