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Keywords = one-dimensional delayed transport equation

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18 pages, 3724 KiB  
Article
Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation
by Karthick Sampath, Subburayan Veerasamy and Ravi P. Agarwal
Symmetry 2022, 14(5), 1046; https://doi.org/10.3390/sym14051046 - 19 May 2022
Cited by 6 | Viewed by 2173
Abstract
In this article, we consider the one-dimensional transport equation with delay and advanced arguments. A maximum principle is proven for the problem considered. As an application of the maximum principle, the stability of the solution is established. It is also proven that the [...] Read more.
In this article, we consider the one-dimensional transport equation with delay and advanced arguments. A maximum principle is proven for the problem considered. As an application of the maximum principle, the stability of the solution is established. It is also proven that the solution’s discontinuity propagates. Finite difference methods with linear interpolation that are conditionally stable and unconditionally stable are presented. This paper presents applications of unconditionally stable numerical methods to symmetric delay arguments and differential equations with variable delays. As a consequence, the matrices of the difference schemes are asymmetric. An illustration of the unconditional stable method is provided with numerical examples. Solution graphs are drawn for all the problems. Full article
(This article belongs to the Special Issue Recent Progress in Studies of Stability of Numerical Schemes)
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