θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems
Our article deals with a new improvement of the [Formula: see text]-parameterized differential transformation method ([Formula: see text] PDTM) by combining it with the Homotopy analysis method (HAM) for solving both the nonlinear initial and the boundary value problems to obtain the optimal values....
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2025.2537475 |
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| author | Ahmed Farooq Qasim Susan H. Mohammad Abdulghafor M. Al-Rozbayani |
| author_facet | Ahmed Farooq Qasim Susan H. Mohammad Abdulghafor M. Al-Rozbayani |
| author_sort | Ahmed Farooq Qasim |
| collection | DOAJ |
| description | Our article deals with a new improvement of the [Formula: see text]-parameterized differential transformation method ([Formula: see text] PDTM) by combining it with the Homotopy analysis method (HAM) for solving both the nonlinear initial and the boundary value problems to obtain the optimal values. The suggested methodology extends the general differential transform method (DTM), enabling the employment of different values of the parameter [Formula: see text] The proposed solution method provides the clear advantage of allowing the original DTM to be divided into several stages, hence demonstrating the specific solution characteristics of nonlinear boundary value problems. Furthermore, the paper also examines and discusses potential alternate solutions derived from various parameter values. To validate the correctness and effectiveness of the approach in rapidly reaching the exact answer, The results of the proposed method were compared with DTM method and exact solutions. |
| format | Article |
| id | doaj-art-2c774fc526cd4a2ca542f79118beaece |
| institution | Kabale University |
| issn | 2576-5299 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj-art-2c774fc526cd4a2ca542f79118beaece2025-08-20T03:34:09ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992025-12-0132126227510.1080/25765299.2025.2537475θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problemsAhmed Farooq Qasim0Susan H. Mohammad1Abdulghafor M. Al-Rozbayani2Departement of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqDepartement of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqDepartement of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqOur article deals with a new improvement of the [Formula: see text]-parameterized differential transformation method ([Formula: see text] PDTM) by combining it with the Homotopy analysis method (HAM) for solving both the nonlinear initial and the boundary value problems to obtain the optimal values. The suggested methodology extends the general differential transform method (DTM), enabling the employment of different values of the parameter [Formula: see text] The proposed solution method provides the clear advantage of allowing the original DTM to be divided into several stages, hence demonstrating the specific solution characteristics of nonlinear boundary value problems. Furthermore, the paper also examines and discusses potential alternate solutions derived from various parameter values. To validate the correctness and effectiveness of the approach in rapidly reaching the exact answer, The results of the proposed method were compared with DTM method and exact solutions.https://www.tandfonline.com/doi/10.1080/25765299.2025.2537475Boundary value problemshomotopy analysis method (HAM)initial value problemsparameterized differential transform method (θ-PDTM) |
| spellingShingle | Ahmed Farooq Qasim Susan H. Mohammad Abdulghafor M. Al-Rozbayani θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems Arab Journal of Basic and Applied Sciences Boundary value problems homotopy analysis method (HAM) initial value problems parameterized differential transform method (θ-PDTM) |
| title | θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| title_full | θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| title_fullStr | θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| title_full_unstemmed | θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| title_short | θ–Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| title_sort | θ parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems |
| topic | Boundary value problems homotopy analysis method (HAM) initial value problems parameterized differential transform method (θ-PDTM) |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2025.2537475 |
| work_keys_str_mv | AT ahmedfarooqqasim thparameterdifferentialtransformwithhomotopyanalysismethodsforsolvingnonlinearinitialandboundaryvalueproblems AT susanhmohammad thparameterdifferentialtransformwithhomotopyanalysismethodsforsolvingnonlinearinitialandboundaryvalueproblems AT abdulghaformalrozbayani thparameterdifferentialtransformwithhomotopyanalysismethodsforsolvingnonlinearinitialandboundaryvalueproblems |