A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations
In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/3309674 |
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| _version_ | 1832561998081032192 |
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| author | Fenglian Liu Muhammad Nadeem Ibrahim Mahariq Suliman Dawood |
| author_facet | Fenglian Liu Muhammad Nadeem Ibrahim Mahariq Suliman Dawood |
| author_sort | Fenglian Liu |
| collection | DOAJ |
| description | In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled with the homotopy perturbation method. This NIS is capable of reducing the linearization, perturbation, and restrictive assumptions that ruin the nature of the numerical problems. Some numerical examples are demonstrated to legitimate the accuracy and authenticity of this NIS. The computational results are obtained in the shape of a series that converges only after a few iterations. The comparison of the graphical representations shows that NIS is a very simple but also an effective approach for other numerical problems involving complex variables. |
| format | Article |
| id | doaj-art-a9d83a4706b54a3cadf89f4bb11f1171 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a9d83a4706b54a3cadf89f4bb11f11712025-02-03T01:23:38ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/3309674A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential EquationsFenglian Liu0Muhammad Nadeem1Ibrahim Mahariq2Suliman Dawood3Institute of Land & Resources and Sustainable DevelopmentSchool of Mathematics and StatisticsCollege of Engineering and TechnologyDepartment of MathematicsIn this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled with the homotopy perturbation method. This NIS is capable of reducing the linearization, perturbation, and restrictive assumptions that ruin the nature of the numerical problems. Some numerical examples are demonstrated to legitimate the accuracy and authenticity of this NIS. The computational results are obtained in the shape of a series that converges only after a few iterations. The comparison of the graphical representations shows that NIS is a very simple but also an effective approach for other numerical problems involving complex variables.http://dx.doi.org/10.1155/2022/3309674 |
| spellingShingle | Fenglian Liu Muhammad Nadeem Ibrahim Mahariq Suliman Dawood A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations Journal of Function Spaces |
| title | A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations |
| title_full | A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations |
| title_fullStr | A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations |
| title_full_unstemmed | A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations |
| title_short | A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations |
| title_sort | numerical approach for the analytical solution of the fourth order parabolic partial differential equations |
| url | http://dx.doi.org/10.1155/2022/3309674 |
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