A numerical method for solving hyperbolic partial differential equations with piecewise constant arguments and variable coefficients. Issue 2 (1st February 2021)

• Record Type: Journal Article
• Authors: Esmailzadeh, M.; Najafi, H. Saberi; Aminikhah, H.
• Is Part Of: Journal of difference equations and applications. Volume 27:Issue 2(2021)
• Page Start: 172
• Page End: 194
• Publication Date: 2021-02-01
• Subjects: Finite difference method -- piecewise constant arguments -- asymptotic stability -- consistency -- convergence -- convergence rate; 65M06 -- 65N06 -- 65L12 -- 65L05; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2021.1881069
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : This article deals with hyperbolic partial differential equations with piecewise constant arguments and variable coefficients. This study, therefore, with the aid of the finite difference technique, aims at presenting a numerical solution scheme for solving such types of equations. The stability, consistency, convergence, and convergence rate of our proposed numerical method are investigated. Moreover, the process of the computation of the analytical solution is studied. In order to support and confirm our theoretical results, some numerical examples are also presented. The figures of the numerical and analytical solutions and also the tables of errors are provided to demonstrate the validity of our proposed scheme.