Finite difference methods with linear interpolation for solving a coupled system of hyperbolic delay differential equations
by S. Karthick; V. Subburayan
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 12, No. 4, 2022

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.

Online publication date: Fri, 28-Oct-2022

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