SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem
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...
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| Format: | Article |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/9053754 |
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| author | Atika Radid Karim Rhofir |
| author_facet | Atika Radid Karim Rhofir |
| author_sort | Atika Radid |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fed3eaf09f7a4595b8f1e57a3eee20b2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fed3eaf09f7a4595b8f1e57a3eee20b22025-02-03T06:46:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/90537549053754SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator ProblemAtika Radid0Karim Rhofir1University Hassan II Casablanca FSAC-MACS, BP. 5366, Maarif Casablanca, MoroccoUniversity Sultan Moulay Slimane LaSTI-ENSA, Bd.Beni Amir, BP.77, Khouribga, MoroccoOur 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.http://dx.doi.org/10.1155/2020/9053754 |
| spellingShingle | Atika Radid Karim Rhofir SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem Discrete Dynamics in Nature and Society |
| title | SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem |
| title_full | SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem |
| title_fullStr | SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem |
| title_full_unstemmed | SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem |
| title_short | SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem |
| title_sort | sor like new iterative method for solving the epidemic model and the prey and predator problem |
| url | http://dx.doi.org/10.1155/2020/9053754 |
| work_keys_str_mv | AT atikaradid sorlikenewiterativemethodforsolvingtheepidemicmodelandthepreyandpredatorproblem AT karimrhofir sorlikenewiterativemethodforsolvingtheepidemicmodelandthepreyandpredatorproblem |