A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems
In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solu...
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| Vydané v: | Mathematics and computers in simulation Ročník 194; s. 505 - 522 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.04.2022
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| ISSN: | 0378-4754, 1872-7166 |
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| Abstract | In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solutions. Numerical comparisons between the proposed algorithm and the standard homotopy approach, as tools for analytically solving reaction–diffusion systems, are performed to test the computational efficiency and the pertinent features of the suggested algorithm. The illustrated numerical results demonstrate that the linearization-based algorithm improves the accuracy and the convergence of the homotopy series solutions. The suggested algorithm can be further used to get rapid convergent series solutions for different types of systems of partial differential equations. |
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| AbstractList | In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solutions. Numerical comparisons between the proposed algorithm and the standard homotopy approach, as tools for analytically solving reaction–diffusion systems, are performed to test the computational efficiency and the pertinent features of the suggested algorithm. The illustrated numerical results demonstrate that the linearization-based algorithm improves the accuracy and the convergence of the homotopy series solutions. The suggested algorithm can be further used to get rapid convergent series solutions for different types of systems of partial differential equations. |
| Author | Shawagfeh, Nabil Odibat, Zaid Al-Qudah, Alaa |
| Author_xml | – sequence: 1 givenname: Alaa surname: Al-Qudah fullname: Al-Qudah, Alaa organization: Department of Mathematics, Faculty of Science, The University of Jordan, Amman, Jordan – sequence: 2 givenname: Zaid orcidid: 0000-0002-2414-7969 surname: Odibat fullname: Odibat, Zaid email: odibat@bau.edu.jo, z.odibat@gmail.com organization: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan – sequence: 3 givenname: Nabil orcidid: 0000-0002-2978-983X surname: Shawagfeh fullname: Shawagfeh, Nabil organization: Department of Mathematics, Faculty of Science, The University of Jordan, Amman, Jordan |
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| Keywords | Reaction–diffusion system Linearization-based algorithm Homotopy analysis method Series solution |
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| Snippet | In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based... |
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| SubjectTerms | Homotopy analysis method Linearization-based algorithm Reaction–diffusion system Series solution |
| Title | A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems |
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