Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead and Allen-Cahn Equations
| dc.contributor.author | Osman, Mohamed S. | |
| dc.contributor.author | Turgut, A. K. | |
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Inan, Bilge | |
| dc.date.accessioned | 2020-05-14T09:38:16Z | |
| dc.date.accessioned | 2025-09-18T15:44:26Z | |
| dc.date.available | 2020-05-14T09:38:16Z | |
| dc.date.available | 2025-09-18T15:44:26Z | |
| dc.date.issued | 2020 | |
| dc.description | Ak, Dr. Turgut/0000-0001-8368-8506; Inan, Bilge/0000-0002-6339-5172; Osman, M. S./0000-0002-5783-0940 | en_US |
| dc.description.abstract | In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell-Whitehead-Segel-type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement. | en_US |
| dc.identifier.citation | Inan, B...et al. (2020). "Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead-Segel and Allen-Cahn Equations",Mathematical Methods In the Applied Sciences, Vol. 43, No. 5, pp. 2588-2600. | en_US |
| dc.identifier.doi | 10.1002/mma.6067 | |
| dc.identifier.issn | 0170-4214 | |
| dc.identifier.issn | 1099-1476 | |
| dc.identifier.scopus | 2-s2.0-85076899839 | |
| dc.identifier.uri | https://doi.org/10.1002/mma.6067 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/14284 | |
| dc.language.iso | en | en_US |
| dc.publisher | Wiley | en_US |
| dc.relation.ispartof | Mathematical Methods in the Applied Sciences | |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Allen-Cahn Equation | en_US |
| dc.subject | Exponential Finite Difference Method | en_US |
| dc.subject | Newell-Whitehead-Segel Equation | en_US |
| dc.subject | Unified Method | en_US |
| dc.title | Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead and Allen-Cahn Equations | en_US |
| dc.title | Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead-Segel and Allen-Cahn Equations | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Ak, Dr. Turgut/0000-0001-8368-8506 | |
| gdc.author.id | Inan, Bilge/0000-0002-6339-5172 | |
| gdc.author.id | Osman, M. S./0000-0002-5783-0940 | |
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| gdc.author.wosid | İnan, Bilge/Lpp-5358-2024 | |
| gdc.author.wosid | Ak, Turgut/A-1086-2019 | |
| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Ak, Dr. Turgut/Z-2129-2018 | |
| gdc.author.wosid | Osman, M. S./E-3084-2013 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Inan, Bilge] Kilis 7 Aralik Univ, Dept Math, Muallim Rifat Fac Educ, Kilis, Turkey; [Osman, Mohamed S.] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt; [Osman, Mohamed S.] Umm Alqura Univ, Fac Appl Sci, Dept Math, Mecca 21955, Saudi Arabia; [Turgut, A. K.] Yalova Univ, Armutlu Vocat Sch, TR-77500 Armutlu, Yalova, Turkey; [Baleanu, Dumitru] Cankaya Univ, Dept Math, Ogretmenler Cad 1406530, Ankara, Turkey; [Baleanu, Dumitru] Inst Space Sci, Magurele, Romania | en_US |
| gdc.description.endpage | 2600 | en_US |
| gdc.description.issue | 5 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.startpage | 2588 | en_US |
| gdc.description.volume | 43 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
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| gdc.oaire.keywords | exponential finite difference method | |
| gdc.oaire.keywords | Error bounds for initial value and initial-boundary value problems involving PDEs | |
| gdc.oaire.keywords | unified method | |
| gdc.oaire.keywords | KdV equations (Korteweg-de Vries equations) | |
| gdc.oaire.keywords | Soliton solutions | |
| gdc.oaire.keywords | PDEs in connection with biology, chemistry and other natural sciences | |
| gdc.oaire.keywords | Finite difference methods for initial value and initial-boundary value problems involving PDEs | |
| gdc.oaire.keywords | Newell-Whitehead-Segel equation | |
| gdc.oaire.keywords | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs | |
| gdc.oaire.keywords | Computational methods for problems pertaining to biology | |
| gdc.oaire.keywords | Allen-Cahn equation | |
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