Computational Approaches to Solving Differential Equations

A special issue of Computation (ISSN 2079-3197).

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 1563

Special Issue Editors


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Guest Editor
Department of Mathematics, British University of Vietnam, Ecopark Campus, 160000 Hung Yen, Hanoi, Vietnam
Interests: mathematical modelling; differential equations; BVP
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Interests: differential and difference equations; dynamical systems; boundary value problems; topological and variational methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential equations, whether ordinary or partial continue to be one of the main areas for research in the field of mathematics. With the increase in popularity of computational methods on mathematical modelling, new approaches and methods are now able to shed a new light on some of the outstanding problems in this area. Areas such as finance, with high frequency trading, computer science and networks with laplace transforms for high-speed connections and even social media with SIR models being applied to model information diffusion are bringing new and challenging problems for discussion.

This Special Issue aims at showcasing both computational and non-computational approaches to those problems, with a clear emphasis on the application aspect of these methods. 

Dr. João Fialho
Prof. Dr. Feliz Manuel Minhós
Guest Editors

Manuscript Submission Information

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Keywords

  • ordinary differential equations
  • BVP
  • partial differential equations
  • mathematical modelling
  • computational methods
  • networks
  • social media information diffusion
  • random DE

Published Papers (1 paper)

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Research

15 pages, 1448 KiB  
Article
Modeling and Simulating an Epidemic in Two Dimensions with an Application Regarding COVID-19
by Khalaf M. Alanazi
Computation 2024, 12(2), 34; https://doi.org/10.3390/computation12020034 - 12 Feb 2024
Viewed by 1179
Abstract
We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. [...] Read more.
We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. To simulate the model in two-dimensional space, we use the continuous Runge–Kutta method of the fourth order and the discrete Runge–Kutta method of the third order with six stages. The numerical results admit the existence of traveling wave solutions for the proposed model. We use the COVID-19 epidemic to conduct numerical experiments and investigate the minimal speed of spread of the traveling wave front. The minimal spreading speeds of COVID-19 are found and discussed. Also, we assess the power of containment measures to contain the epidemic. The results depict a clear drop in the spreading speed of the traveling wave front after applying containment measures to at-risk populations. Full article
(This article belongs to the Special Issue Computational Approaches to Solving Differential Equations)
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