A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem
In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30068/1/A%20three.pdf |
| _version_ | 1796971666834718720 |
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| author | Mechee, Mohammed Senu, Norazak Ismail, Fudziah Nikouravan, B. Siri, Zailan |
| author_facet | Mechee, Mohammed Senu, Norazak Ismail, Fudziah Nikouravan, B. Siri, Zailan |
| author_sort | Mechee, Mohammed |
| collection | UPM |
| description | In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method. |
| first_indexed | 2024-03-06T08:16:23Z |
| format | Article |
| id | upm.eprints-30068 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T08:16:23Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-300682015-10-09T07:02:56Z http://psasir.upm.edu.my/id/eprint/30068/ A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem Mechee, Mohammed Senu, Norazak Ismail, Fudziah Nikouravan, B. Siri, Zailan In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30068/1/A%20three.pdf Mechee, Mohammed and Senu, Norazak and Ismail, Fudziah and Nikouravan, B. and Siri, Zailan (2013) A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem. Mathematical Problems in Engineering, 2013. art. no. 795397. pp. 1-7. ISSN 1024-123X http://www.hindawi.com/journals/mpe/2013/795397/ 10.1155/2013/795397 English |
| spellingShingle | Mechee, Mohammed Senu, Norazak Ismail, Fudziah Nikouravan, B. Siri, Zailan A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title | A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title_full | A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title_fullStr | A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title_full_unstemmed | A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title_short | A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem |
| title_sort | three stage fifth order runge kutta method for directly solving special third order differential equation with application to thin film flow problem |
| url | http://psasir.upm.edu.my/id/eprint/30068/1/A%20three.pdf |
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