Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation
In this article, we present a novel enhancement to the α-parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. Our...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/3339655 |
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| author | Abdulghafor M. Al-Rozbayani Ahmed Farooq Qasim |
| author_facet | Abdulghafor M. Al-Rozbayani Ahmed Farooq Qasim |
| author_sort | Abdulghafor M. Al-Rozbayani |
| collection | DOAJ |
| description | In this article, we present a novel enhancement to the α-parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. Our proposed approach extends the general differential transformation method, allowing for the use of various values for the coefficient α. Our solution procedure offers a distinct advantage by allowing the original differential transformation method to be divided into multiple steps, thereby illustrating specific solution properties for nonlinear boundary value problems. Additionally, possible alternative solutions based on varying parameter values are also explored and discussed. The results with those obtained through the DTM method and exact solutions are compared to confirm the accuracy of our method and its efficiency in reaching the exact solution quickly. |
| format | Article |
| id | doaj-art-dacfe1c01daa4fb09a830b419ad92b8d |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-dacfe1c01daa4fb09a830b419ad92b8d2025-02-03T06:45:14ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/3339655Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner EquationAbdulghafor M. Al-Rozbayani0Ahmed Farooq Qasim1Department of MathematicsDepartment of MathematicsIn this article, we present a novel enhancement to the α-parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. Our proposed approach extends the general differential transformation method, allowing for the use of various values for the coefficient α. Our solution procedure offers a distinct advantage by allowing the original differential transformation method to be divided into multiple steps, thereby illustrating specific solution properties for nonlinear boundary value problems. Additionally, possible alternative solutions based on varying parameter values are also explored and discussed. The results with those obtained through the DTM method and exact solutions are compared to confirm the accuracy of our method and its efficiency in reaching the exact solution quickly.http://dx.doi.org/10.1155/2023/3339655 |
| spellingShingle | Abdulghafor M. Al-Rozbayani Ahmed Farooq Qasim Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation Journal of Applied Mathematics |
| title | Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation |
| title_full | Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation |
| title_fullStr | Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation |
| title_full_unstemmed | Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation |
| title_short | Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation |
| title_sort | modified α parameterized differential transform method for solving nonlinear generalized gardner equation |
| url | http://dx.doi.org/10.1155/2023/3339655 |
| work_keys_str_mv | AT abdulghaformalrozbayani modifiedaparameterizeddifferentialtransformmethodforsolvingnonlineargeneralizedgardnerequation AT ahmedfarooqqasim modifiedaparameterizeddifferentialtransformmethodforsolvingnonlineargeneralizedgardnerequation |