Title: Finite difference methods with linear interpolation for solving a coupled system of hyperbolic delay differential equations

Authors: S. Karthick; V. Subburayan

Addresses: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603203, Tamil Nadu, India ' Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603203, Tamil Nadu, India

Abstract: In this article a system of first-order hyperbolic delay differential equations is considered. The maximum principle is proved for the problem considered. Further, the stability of the solution is established as an application of the maximum principle. The propagation of the discontinuity of the solution is also established. A piecewise uniform mesh is designed for solving the problem. On the piecewise uniform mesh, conditionally stable and unconditionally stable finite difference methods with piecewise linear interpolation are suggested to solve the problem. It is proved that the methods are consistent, stable, and convergent. Numerical illustrative examples are given to validate the theoretical results.

Keywords: hyperbolic system; delay differential equations; conditional method; unconditional method; linear interpolation; maximum principle; piecewise linear interpolation.

DOI: 10.1504/IJMMNO.2022.126557

International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.4, pp.370 - 389

Received: 30 Sep 2021
Accepted: 07 Apr 2022
Published online: 28 Oct 2022 *

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