A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations
We present a new form of fourth-order explicit Runge-Kutta method in which the terms f and f′ are used in the formulae to increase the order as well as to enhance the performance of the method. The proposed method is then used to solve first order ordinary differential equation of the form y' =...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2012
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57410/ http://psasir.upm.edu.my/id/eprint/57410/1/A%20new%20fourth-order%20explicit%20Runge-Kutta%20method%20for%20solving%20first%20order%20ordinary%20differential%20equations.pdf |
| _version_ | 1848853358492778496 |
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| author | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak |
| author_facet | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak |
| author_sort | Jikantoro, Yusuf Dauda |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We present a new form of fourth-order explicit Runge-Kutta method in which the terms f and f′ are used in the formulae to increase the order as well as to enhance the performance of the method. The proposed method is then used to solve first order ordinary differential equation of the form y' = f(t,y(t)). From the numerical results, it is observed that the new method is more efficient in terms of time needed for solving the problems while maintaining the same accuracy as the existing Runge-Kutta method of the same order. Stability of the method is discussed the region of absolute stability is shown. |
| first_indexed | 2025-11-15T10:52:42Z |
| format | Conference or Workshop Item |
| id | upm-57410 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:42Z |
| publishDate | 2012 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-574102017-09-27T09:21:51Z http://psasir.upm.edu.my/id/eprint/57410/ A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak We present a new form of fourth-order explicit Runge-Kutta method in which the terms f and f′ are used in the formulae to increase the order as well as to enhance the performance of the method. The proposed method is then used to solve first order ordinary differential equation of the form y' = f(t,y(t)). From the numerical results, it is observed that the new method is more efficient in terms of time needed for solving the problems while maintaining the same accuracy as the existing Runge-Kutta method of the same order. Stability of the method is discussed the region of absolute stability is shown. AIP Publishing LLC 2012 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57410/1/A%20new%20fourth-order%20explicit%20Runge-Kutta%20method%20for%20solving%20first%20order%20ordinary%20differential%20equations.pdf Jikantoro, Yusuf Dauda and Ismail, Fudziah and Senu, Norazak (2012) A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations. In: 20th National Symposium on Mathematical Sciences (SKSM20), 18-20 Dec. 2012, Palm Garden Hotel, Putrajaya, Malaysia. (pp. 1003-1010). 10.1063/1.4801239 |
| spellingShingle | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title | A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title_full | A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title_fullStr | A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title_full_unstemmed | A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title_short | A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations |
| title_sort | new fourth-order explicit runge-kutta method for solving first order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/57410/ http://psasir.upm.edu.my/id/eprint/57410/ http://psasir.upm.edu.my/id/eprint/57410/1/A%20new%20fourth-order%20explicit%20Runge-Kutta%20method%20for%20solving%20first%20order%20ordinary%20differential%20equations.pdf |