A numerical method for solving hyperbolic partial differential equations with piecewise constant arguments and variable coefficients

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, co...

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Bibliographic Details
Published in:Journal of difference equations and applications 2021-02, Vol.27 (2), p.172-194
Main Authors: Esmailzadeh, M., Najafi, H. Saberi, Aminikhah, H.
Format: Article
Language:English
Subjects:
asymptotic stability
consistency
Convergence
convergence rate
Exact solutions
Finite difference method
Numerical analysis
Numerical methods
Partial differential equations
piecewise constant arguments
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Summary: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.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2021.1881069