Direct numerical methods for solving a class of third-order partial differential equations
In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a fla...
| Main Authors: | , , , |
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| Format: | Article |
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Elsevier
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/37113/ |
| _version_ | 1848848521201975296 |
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| author | Mechee, M. Ismail, F. Hussain, Z. M. Siri, Z. |
| author_facet | Mechee, M. Ismail, F. Hussain, Z. M. Siri, Z. |
| author_sort | Mechee, M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a flat plate. An efficient numerical method is proposed for PDE of type I. The PDE of type I is converted to a system of third-order ordinary differential equations (ODEs) using the method of lines. The system of ODEs is then solved using direct Runge–Kutta which we derived purposely for solving special third-order ODEs of the form y''' = f(x,y). Simulation results showed that the proposed RKD-based method is more accurate than the existing finite difference method. |
| first_indexed | 2025-11-15T09:35:49Z |
| format | Article |
| id | upm-37113 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T09:35:49Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-371132023-09-04T07:38:25Z http://psasir.upm.edu.my/id/eprint/37113/ Direct numerical methods for solving a class of third-order partial differential equations Mechee, M. Ismail, F. Hussain, Z. M. Siri, Z. In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a flat plate. An efficient numerical method is proposed for PDE of type I. The PDE of type I is converted to a system of third-order ordinary differential equations (ODEs) using the method of lines. The system of ODEs is then solved using direct Runge–Kutta which we derived purposely for solving special third-order ODEs of the form y''' = f(x,y). Simulation results showed that the proposed RKD-based method is more accurate than the existing finite difference method. Elsevier 2014 Article PeerReviewed Mechee, M. and Ismail, F. and Hussain, Z. M. and Siri, Z. (2014) Direct numerical methods for solving a class of third-order partial differential equations. Applied Mathematics and Computation, 247. pp. 663-674. ISSN 0096-3003; ESSN: 1873-5649 https://www.sciencedirect.com/science/article/pii/S0096300314012399 10.1016/j.amc.2014.09.021 |
| spellingShingle | Mechee, M. Ismail, F. Hussain, Z. M. Siri, Z. Direct numerical methods for solving a class of third-order partial differential equations |
| title | Direct numerical methods for solving a class of third-order partial differential equations |
| title_full | Direct numerical methods for solving a class of third-order partial differential equations |
| title_fullStr | Direct numerical methods for solving a class of third-order partial differential equations |
| title_full_unstemmed | Direct numerical methods for solving a class of third-order partial differential equations |
| title_short | Direct numerical methods for solving a class of third-order partial differential equations |
| title_sort | direct numerical methods for solving a class of third-order partial differential equations |
| url | http://psasir.upm.edu.my/id/eprint/37113/ http://psasir.upm.edu.my/id/eprint/37113/ http://psasir.upm.edu.my/id/eprint/37113/ |