Modified two-dimensional differential transform method for solving proportional delay partial differential equations
In this study, we develop a modified version of the two-dimensional differential transform (TDDT) method for solving proportional delay partial differential equations (PDPDEs) that frequently arise in engineering and scientific models. This modification is achieved by integrating the TDDT method wit...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720724001292 |
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| author | Osama Ala’yed |
| author_facet | Osama Ala’yed |
| author_sort | Osama Ala’yed |
| collection | DOAJ |
| description | In this study, we develop a modified version of the two-dimensional differential transform (TDDT) method for solving proportional delay partial differential equations (PDPDEs) that frequently arise in engineering and scientific models. This modification is achieved by integrating the TDDT method with the Laplace transform and the Padé approximant, thereby leveraging the strengths of each technique to improve overall performance. Theorems are provided in a general manner to cover various types of PDEs, with constant or variable coefficients. To validate the approach, we apply it to three test problems, demonstrating its effectiveness in extending the convergence domain of the traditional TDDT approach, reducing computational complexity, and yielding analytic solutions with fewer computational steps. Results indicate that the method is a viable alternative for addressing PDPDEs, especially in scenarios where traditional analytic solutions are challenging to obtain. This combination opens new avenues for efficiently solving complex delayed systems in engineering and science, potentially outperforming existing numerical and analytical techniques in both speed and reliability. |
| format | Article |
| id | doaj-art-3b9b3b18cd7b4bdd83c9dab7323c4fe1 |
| institution | Kabale University |
| issn | 2666-7207 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-3b9b3b18cd7b4bdd83c9dab7323c4fe12024-12-17T05:01:22ZengElsevierResults in Control and Optimization2666-72072024-12-0117100499Modified two-dimensional differential transform method for solving proportional delay partial differential equationsOsama Ala’yed0Department of Mathematics, Jadara University, Irbid, 21110, JordanIn this study, we develop a modified version of the two-dimensional differential transform (TDDT) method for solving proportional delay partial differential equations (PDPDEs) that frequently arise in engineering and scientific models. This modification is achieved by integrating the TDDT method with the Laplace transform and the Padé approximant, thereby leveraging the strengths of each technique to improve overall performance. Theorems are provided in a general manner to cover various types of PDEs, with constant or variable coefficients. To validate the approach, we apply it to three test problems, demonstrating its effectiveness in extending the convergence domain of the traditional TDDT approach, reducing computational complexity, and yielding analytic solutions with fewer computational steps. Results indicate that the method is a viable alternative for addressing PDPDEs, especially in scenarios where traditional analytic solutions are challenging to obtain. This combination opens new avenues for efficiently solving complex delayed systems in engineering and science, potentially outperforming existing numerical and analytical techniques in both speed and reliability.http://www.sciencedirect.com/science/article/pii/S2666720724001292Two-dimensional differential transform methodModified two-dimensional differential transform methodProportional delay partial differential equationsLaplace transformPadé approximant |
| spellingShingle | Osama Ala’yed Modified two-dimensional differential transform method for solving proportional delay partial differential equations Results in Control and Optimization Two-dimensional differential transform method Modified two-dimensional differential transform method Proportional delay partial differential equations Laplace transform Padé approximant |
| title | Modified two-dimensional differential transform method for solving proportional delay partial differential equations |
| title_full | Modified two-dimensional differential transform method for solving proportional delay partial differential equations |
| title_fullStr | Modified two-dimensional differential transform method for solving proportional delay partial differential equations |
| title_full_unstemmed | Modified two-dimensional differential transform method for solving proportional delay partial differential equations |
| title_short | Modified two-dimensional differential transform method for solving proportional delay partial differential equations |
| title_sort | modified two dimensional differential transform method for solving proportional delay partial differential equations |
| topic | Two-dimensional differential transform method Modified two-dimensional differential transform method Proportional delay partial differential equations Laplace transform Padé approximant |
| url | http://www.sciencedirect.com/science/article/pii/S2666720724001292 |
| work_keys_str_mv | AT osamaalayed modifiedtwodimensionaldifferentialtransformmethodforsolvingproportionaldelaypartialdifferentialequations |