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Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems

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Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain
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Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Apdo. 99, 03080 Alicante, Spain
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1038; https://doi.org/10.3390/math7111038
Received: 5 September 2019 / Revised: 25 October 2019 / Accepted: 27 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue Models of Delay Differential Equations)
In recent works, exact and nonstandard finite difference schemes for scalar first order linear delay differential equations have been proposed. The aim of the present work is to extend these previous results to systems of coupled delay differential equations X ( t ) = A X ( t ) + B X ( t τ ) , where X is a vector, and A and B are commuting real matrices, in general not simultaneously diagonalizable. Based on a constructive expression for the exact solution of the vector equation, an exact scheme is obtained, and different nonstandard numerical schemes of increasing order are proposed. Dynamic consistency properties of the new nonstandard schemes are illustrated with numerical examples, and proved for a class of methods. View Full-Text
Keywords: delay systems; nonstandard numerical methods; dynamic consistency delay systems; nonstandard numerical methods; dynamic consistency
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Castro, M.Á.; García, M.A.; Martín, J.A.; Rodríguez, F. Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems. Mathematics 2019, 7, 1038.

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