Exact and nonstandard numerical schemes for linear delay differential models

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Title: Exact and nonstandard numerical schemes for linear delay differential models
Authors: García Ferrández, Miguel Antonio | Castro, María Ángeles | 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
Keywords: Delay differential equations | Nonstandard finite difference methods | Dynamic consistency
Knowledge Area: Matemática Aplicada
Issue Date: 1-Dec-2018
Publisher: Elsevier
Citation: Applied Mathematics and Computation. 2018, 338: 337-345. doi:10.1016/j.amc.2018.06.029
Abstract: Delay differential models present characteristic dynamical properties that should ideally be preserved when computing numerical approximate solutions. In this work, exact numerical schemes for a general linear delay differential model, as well as for the special case of a pure delay model, are obtained. Based on these exact schemes, a family of nonstandard methods, of increasing order of accuracy and simple computational properties, is proposed. Dynamic consistency of the new nonstandard methods are proved, and illustrated with numerical examples, for asymptotic stability, positive preserving properties, and oscillation behaviour.
Sponsor: This work was partially funded by grant GRE12-08 from University of Alicante.
URI: http://hdl.handle.net/10045/77208
ISSN: 0096-3003 (Print) | 1873-5649 (Online)
DOI: 10.1016/j.amc.2018.06.029
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2018 Elsevier Inc.
Peer Review: si
Publisher version: https://doi.org/10.1016/j.amc.2018.06.029
Appears in Collections:INV - EDR - Artículos de Revistas
INV - ADMPBG - Artículos de Revistas

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