A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM)
ABSTRACT The Buckmaster equation, a nonlinear partial differential equation (PDE) central to modeling the dynamics and deformation of flat fluid plates, presents significant analytical and computational challenges due to its inherent complexity. Traditional solution approaches predominantly rely on...
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Wiley
2025-03-01
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| Online Access: | https://doi.org/10.1002/eng2.70044 |
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| author | Kabir Oluwatobi Idowu Abdullateef Adedeji Adedapo Christopher Loyinmi Guang Lin |
| author_facet | Kabir Oluwatobi Idowu Abdullateef Adedeji Adedapo Christopher Loyinmi Guang Lin |
| author_sort | Kabir Oluwatobi Idowu |
| collection | DOAJ |
| description | ABSTRACT The Buckmaster equation, a nonlinear partial differential equation (PDE) central to modeling the dynamics and deformation of flat fluid plates, presents significant analytical and computational challenges due to its inherent complexity. Traditional solution approaches predominantly rely on numerical methods, which, although effective, are often computationally intensive and face limitations in handling nonlinearity. In this study, we propose and apply the Elzaki projected differential transform method (EPDTM), a semi‐analytic approach, to solve the Buckmaster equation. The EPDTM combines the strengths of the Elzaki transform and the projected differential transform method, offering a precise and computationally efficient framework to tackle such nonlinear equations. We present approximate solutions for two specific cases of the Buckmaster equation and generalize our analysis to its broader form. A detailed comparative analysis of the EPDTM results with exact solutions, using tables, 3D plots, and error graphs, demonstrates the negligible absolute errors achieved by the method. Convergence plots further validate the rapid alignment of the EPDTM solutions with the exact solutions, showcasing their accuracy and reliability. Compared with existing numerical methods, EPDTM significantly reduces computational demand while maintaining high precision, even when handling nonlinearity. The findings underscore the potential of the EPDTM as a robust and efficient tool for solving complex nonlinear PDEs such as the Buckmaster equation. This method provides an effective alternative to traditional numerical approaches and opens new opportunities for its application in broader mathematical modeling and scientific domains. |
| format | Article |
| id | doaj-art-6b71bcbcb5dc433d9bfbfaf461d46f91 |
| institution | DOAJ |
| issn | 2577-8196 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Wiley |
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| spelling | doaj-art-6b71bcbcb5dc433d9bfbfaf461d46f912025-08-20T02:54:02ZengWileyEngineering Reports2577-81962025-03-0173n/an/a10.1002/eng2.70044A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM)Kabir Oluwatobi Idowu0Abdullateef Adedeji1Adedapo Christopher Loyinmi2Guang Lin3Department of Mathematics Purdue University West Lafayette Indiana USADepartment of Mathematics Tai Solarin University of Education, Ijagun Ijebu Ode Ogun State NigeriaDepartment of Mathematics Tai Solarin University of Education, Ijagun Ijebu Ode Ogun State NigeriaDepartment of Mathematics, School of Mechanical Engineering Purdue University West Lafayette Indiana USAABSTRACT The Buckmaster equation, a nonlinear partial differential equation (PDE) central to modeling the dynamics and deformation of flat fluid plates, presents significant analytical and computational challenges due to its inherent complexity. Traditional solution approaches predominantly rely on numerical methods, which, although effective, are often computationally intensive and face limitations in handling nonlinearity. In this study, we propose and apply the Elzaki projected differential transform method (EPDTM), a semi‐analytic approach, to solve the Buckmaster equation. The EPDTM combines the strengths of the Elzaki transform and the projected differential transform method, offering a precise and computationally efficient framework to tackle such nonlinear equations. We present approximate solutions for two specific cases of the Buckmaster equation and generalize our analysis to its broader form. A detailed comparative analysis of the EPDTM results with exact solutions, using tables, 3D plots, and error graphs, demonstrates the negligible absolute errors achieved by the method. Convergence plots further validate the rapid alignment of the EPDTM solutions with the exact solutions, showcasing their accuracy and reliability. Compared with existing numerical methods, EPDTM significantly reduces computational demand while maintaining high precision, even when handling nonlinearity. The findings underscore the potential of the EPDTM as a robust and efficient tool for solving complex nonlinear PDEs such as the Buckmaster equation. This method provides an effective alternative to traditional numerical approaches and opens new opportunities for its application in broader mathematical modeling and scientific domains.https://doi.org/10.1002/eng2.70044Buckmaster equationElzaki transformprojected differential transformsemi‐analytic |
| spellingShingle | Kabir Oluwatobi Idowu Abdullateef Adedeji Adedapo Christopher Loyinmi Guang Lin A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) Engineering Reports Buckmaster equation Elzaki transform projected differential transform semi‐analytic |
| title | A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) |
| title_full | A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) |
| title_fullStr | A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) |
| title_full_unstemmed | A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) |
| title_short | A Semi‐Analytic Hybrid Approach for Solving the Buckmaster Equation: Application of the Elzaki Projected Differential Transform Method (EPDTM) |
| title_sort | semi analytic hybrid approach for solving the buckmaster equation application of the elzaki projected differential transform method epdtm |
| topic | Buckmaster equation Elzaki transform projected differential transform semi‐analytic |
| url | https://doi.org/10.1002/eng2.70044 |
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