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Open AccessArticle

On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

1
Department of Mathematics, Near East University, Lefkosa, Mersin 10 99138, Turkey
2
Department of Mathematics, Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia
3
Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(6), 1033; https://doi.org/10.3390/sym12061033
Received: 16 April 2020 / Revised: 29 May 2020 / Accepted: 15 June 2020 / Published: 19 June 2020
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested. View Full-Text
Keywords: time delay; third order differential equations; difference scheme; stability time delay; third order differential equations; difference scheme; stability
MDPI and ACS Style

Ashyralyev, A.; Hınçal, E.; Ibrahim, S. On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations. Symmetry 2020, 12, 1033.

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