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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2576-5299 |