Special Issue "Models of Delay Differential Equations"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 January 2020.

Special Issue Editors

Prof. Francisco Rodríguez
E-Mail Website
Guest Editor
Department of Applied Mathematics and Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Apdo. 99, Alicante 03080, Spain
Interests: delay differential equations; diffusion and heat conduction models with delay; mathematical biology
Prof. Juan Carlos Cortés López
E-Mail Website
Guest Editor
Department of Applied Mathematics and Institute for Multidisciplinary Mathematics (im2), Polytechnic University of Valencia, 46022 Valencia, Spain
Interests: random delay differential equations; uncertainty quantification with delay differential equations; mathematical modeling with delay differential equations
Special Issues and Collections in MDPI journals
Prof. María Ángeles Castro
E-Mail Website
Guest Editor
Department of Applied Mathematics, University of Alicante, Apdo. 99, Alicante 03080, Spain
Interests: delay differential equations; numerical methods; non-Fourier heat conduction models

Special Issue Information

Dear Colleagues,

Models of differential equations with delay have pervaded many scientific and technical fields in the last decades. The use of delay differential equations (DDE) and partial delay differential equations (PDDE) to model problems with the presence of lags or hereditary effects have demonstrated a valuable balance between realism and tractability. Of special interest in recent years is the development and analysis of models with interactions between delay and random effects, through the use of stochastic and random delay differential equation (SDDE and RDDE). In this Special Issue, we are inviting submissions of original papers dealing with the theory and applications of differential equations with delay (DDE, PDDE, SDDE, and RDDE), including, but not limited to, construction of exact solutions, numerical methods, dynamical properties, and applications to mathematical modeling of phenomena and processes in biology, medicine, economics, engineering, and the social sciences.

Prof. Francisco Rodríguez
Prof. Juan Carlos Cortés López
Prof. María Ángeles Castro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Delay differential equations
  • Partial delay differential equations
  • Random and stochastic delay differential equations
  • Numerical methods
  • Exact solutions and dynamical properties
  • Diffusion and heat conduction models with delay
  • Uncertainty quantification with delay differential equations and simulation
  • Models with delay in biology, economics, and engineering

Published Papers (2 papers)

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Research

Open AccessArticle
Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations
Mathematics 2019, 7(12), 1163; https://doi.org/10.3390/math7121163 - 02 Dec 2019
Abstract
In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential problem for a semilinear [...] Read more.
In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential problem for a semilinear hyperbolic equation with unbounded time delay term is established. In applications, the existence and uniqueness of bounded solutions of four problems for semilinear hyperbolic equations with time delay in unbounded term are obtained. For the approximate solution of this abstract differential problem, the two-step difference scheme of a first order of accuracy is presented. The mean theorem on the existence and uniqueness of a uniformly bounded solution of this difference scheme with respect to time stepsize is established. In applications, the existence and uniqueness of a uniformly bounded solutions with respect to time and space stepsizes of difference schemes for four semilinear partial differential equations with time delay in unbounded term are obtained. In general, it is not possible to get the exact solution of semilinear hyperbolic equations with unbounded time delay term. Therefore, numerical results for the solution of difference schemes for one and two dimensional semilinear hyperbolic equation with time delay are presented. Finally, some numerical examples are given to confirm the theoretical analysis. Full article
(This article belongs to the Special Issue Models of Delay Differential Equations)
Open AccessArticle
Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems
Mathematics 2019, 7(11), 1038; https://doi.org/10.3390/math7111038 - 03 Nov 2019
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Models of Delay Differential Equations)
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