Direct numerical method for solving a class of fourth-order partial differential equation
In this paper, we classified a class of fourth-order partial differential equations (PDEs) to be fourth-order PDE of type I, II, III and IV. The PDE of type IV is solved by using an efficient numerical method. The PDE is first transformed to a system of fourth-order ordinary differential equations (...
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| Format: | Article |
| Language: | English |
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Research India Publications
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/55534/1/Direct%20numerical%20method%20for%20solving%20a%20class%20of%20fourth-order%20partial%20differential%20equation.pdf |
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| author | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak |
| author_facet | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak |
| author_sort | Hussain, Kasim Abbas |
| collection | UPM |
| description | In this paper, we classified a class of fourth-order partial differential equations (PDEs) to be fourth-order PDE of type I, II, III and IV. The PDE of type IV is solved by using an efficient numerical method. The PDE is first transformed to a system of fourth-order ordinary differential equations (ODEs) using the method of lines, then the resulting system of fourth-order ODEs is solved using direct Runge-Kutta method (RKFD). The RKFD method is constructed purposely for solving special fourth-order ODEs. Numerical results demonstrated that the RKFD method is in good agreement with the exact solutions. |
| first_indexed | 2024-03-06T09:23:42Z |
| format | Article |
| id | upm.eprints-55534 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:23:42Z |
| publishDate | 2016 |
| publisher | Research India Publications |
| record_format | dspace |
| spelling | upm.eprints-555342017-09-13T02:27:27Z http://psasir.upm.edu.my/id/eprint/55534/ Direct numerical method for solving a class of fourth-order partial differential equation Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak In this paper, we classified a class of fourth-order partial differential equations (PDEs) to be fourth-order PDE of type I, II, III and IV. The PDE of type IV is solved by using an efficient numerical method. The PDE is first transformed to a system of fourth-order ordinary differential equations (ODEs) using the method of lines, then the resulting system of fourth-order ODEs is solved using direct Runge-Kutta method (RKFD). The RKFD method is constructed purposely for solving special fourth-order ODEs. Numerical results demonstrated that the RKFD method is in good agreement with the exact solutions. Research India Publications 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/55534/1/Direct%20numerical%20method%20for%20solving%20a%20class%20of%20fourth-order%20partial%20differential%20equation.pdf Hussain, Kasim Abbas and Ismail, Fudziah and Senu, Norazak (2016) Direct numerical method for solving a class of fourth-order partial differential equation. Global Journal of Pure and Applied Mathematics, 12 (2). pp. 1257-1272. ISSN 0973-1768; ESSN: 0973-9750 https://www.ripublication.com/gjpam16/gjpamv12n2_07.pdf |
| spellingShingle | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Direct numerical method for solving a class of fourth-order partial differential equation |
| title | Direct numerical method for solving a class of fourth-order partial differential equation |
| title_full | Direct numerical method for solving a class of fourth-order partial differential equation |
| title_fullStr | Direct numerical method for solving a class of fourth-order partial differential equation |
| title_full_unstemmed | Direct numerical method for solving a class of fourth-order partial differential equation |
| title_short | Direct numerical method for solving a class of fourth-order partial differential equation |
| title_sort | direct numerical method for solving a class of fourth order partial differential equation |
| url | http://psasir.upm.edu.my/id/eprint/55534/1/Direct%20numerical%20method%20for%20solving%20a%20class%20of%20fourth-order%20partial%20differential%20equation.pdf |
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