SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-18
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Our aim in this paper is to propose an SOR-like new iterative method by introducing a relaxation parameter ω to improve the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [J.
Math.
Anal.
Appl.
316 (2006) 753–763] in order to solve two problems.
The first one is the problem of the spread of a nonfatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of prey and predator.
The proposed method is not limited to these two problems but can be applicable to a wide range of systems of nonlinear functional problem.
The results, for different values of ω, show that we found some known methods and our method compared to methods using the calculation of special polynomials and derivatives like the Adomian decomposition method (ADM), the calculation of the Lagrange multiplier as in the variational iterative method (VIM), or the construction of a homotopy as in the homotopy perturbation method (HPM) has several advantages, such as very effective and very simple to implement.
Unfortunately, these methods do not guarantee a valid approximation in large time interval.
To overcome this, we applied our method for approximating the solution of the problems in a sequence of time intervals as a multistage approach.
Some numerical results are presented with plots according to the parameter ω.
American Psychological Association (APA)
Radid, Atika& Rhofir, Karim. 2020. SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1153594
Modern Language Association (MLA)
Radid, Atika& Rhofir, Karim. SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1153594
American Medical Association (AMA)
Radid, Atika& Rhofir, Karim. SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1153594
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153594