On the Construction of Exact Numerical Schemes for Linear Delay Models
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Título: | On the Construction of Exact Numerical Schemes for Linear Delay Models |
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Autor/es: | Mayorga, Carlos Julio | Castro, María Ángeles | Sirvent Guijarro, Antonio | Rodríguez, Francisco |
Grupo/s de investigación o GITE: | Modelización de Procesos en Biogeociencias y Ecuaciones Diferenciales con Retardo (MODDE) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemática Aplicada | Universidad de Alicante. Instituto Multidisciplinar para el Estudio del Medio "Ramón Margalef" |
Palabras clave: | Exact numerical schemes | Neutral delay differential equations | Fundamental solutions |
Fecha de publicación: | 12-abr-2023 |
Editor: | MDPI |
Cita bibliográfica: | Mayorga CJ, Castro MÁ, Sirvent A, Rodríguez F. On the Construction of Exact Numerical Schemes for Linear Delay Models. Mathematics. 2023; 11(8):1836. https://doi.org/10.3390/math11081836 |
Resumen: | Exact numerical schemes have previously been obtained for some linear retarded delay differential equations and systems. Those schemes were derived from explicit expressions of the exact solutions, and were expressed in the form of perturbed difference systems, involving the values at previous delay intervals. In this work, we propose to directly obtain expressions of the same type for the fundamental solutions of linear delay differential equations, by considering vector equations with vector components corresponding to delay-lagged values at previous intervals. From these expressions for the fundamental solutions, exact numerical schemes for arbitrary initial functions can be proposed, and they may also facilitate obtaining explicit exact solutions. We apply this approach to obtain an exact numerical scheme for the first order linear neutral equation x′(t)−γx′(t−τ)=αx(t)+βx(t−τ), with the general initial condition x(t)=φ(t) for −τ≤t≤0. The resulting expression reduces to those previously published for the corresponding retarded equations when γ=0. |
Patrocinador/es: | This research was partly funded by “MCIN/AEI/10.13039/501100011033 (Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación), grant number PID2021-125517OB-I00”; and by “Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital, Generalitat Valenciana, grant number CIPROM/2021/001”. |
URI: | http://hdl.handle.net/10045/133827 |
ISSN: | 2227-7390 |
DOI: | 10.3390/math11081836 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2023 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 (https://creativecommons.org/licenses/by/4.0/). |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.3390/math11081836 |
Aparece en las colecciones: | INV - MODDE - Artículos de Revistas |
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