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

María Ángeles Castro, Miguel Antonio García, José Antonio Martín and Francisco Rodríguez
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María Ángeles Castro: Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain
Miguel Antonio García: Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain
José Antonio Martín: Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain
Francisco Rodríguez: Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain

Mathematics, 2019, vol. 7, issue 11, 1-14

Abstract: 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.

Keywords: delay systems; nonstandard numerical methods; dynamic consistency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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