Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems
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Title: | Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems |
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Authors: | Castro, María Ángeles | García Ferrández, Miguel Antonio | Martín Alustiza, José Antonio | Rodríguez, Francisco |
Research Group/s: | Análisis de Datos y Modelización de Procesos en Biología y Geociencias | Ecuaciones Diferenciales con Retardo |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemática Aplicada | Universidad de Alicante. Instituto Multidisciplinar para el Estudio del Medio "Ramón Margalef" |
Keywords: | Delay systems | Nonstandard numerical methods | Dynamic consistency |
Knowledge Area: | Matemática Aplicada |
Issue Date: | 3-Nov-2019 |
Publisher: | MDPI |
Citation: | Castro MÁ, García MA, Martín JA, Rodríguez F. Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems. Mathematics. 2019; 7(11):1038. doi:10.3390/math7111038 |
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)=AX(t)+BX(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. |
Sponsor: | This research was funded by Ministerio de Economía y Competitividad grant number CGL2017-89804-R. |
URI: | http://hdl.handle.net/10045/98568 |
ISSN: | 2227-7390 |
DOI: | 10.3390/math7111038 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Peer Review: | si |
Publisher version: | https://doi.org/10.3390/math7111038 |
Appears in Collections: | INV - EDR - Artículos de Revistas INV - MODDE - Artículos de Revistas |
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2019_Castro_etal_Mathematics.pdf | 3,42 MB | Adobe PDF | Open Preview | |
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