Fourth order 4-stages improved Runge-Kutta method with minimized error norm
In this paper the improved Runge-Kutta method of order four with 4-stages for solving first order ordinary differential equation is proposed. The method is based on classical Runge-Kutta (RK) method also can be considered as special class of two-step method. Here, the coefficients of the method are...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57196/ http://psasir.upm.edu.my/id/eprint/57196/1/Fourth%20order%204-stages%20improved%20Runge-Kutta%20method%20with%20minimized%20error%20norm.pdf |
| _version_ | 1848853297625038848 |
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| author | Rabiei, Faranak Ismail, Fudziah |
| author_facet | Rabiei, Faranak Ismail, Fudziah |
| author_sort | Rabiei, Faranak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper the improved Runge-Kutta method of order four with 4-stages for solving first order ordinary differential equation is proposed. The method is based on classical Runge-Kutta (RK) method also can be considered as special class of two-step method. Here, the coefficients of the method are obtained using the minimization of the error norm up to order five. The improved method with only 4-stages is more accurate than fourth order 4-stages RK method. Therefore it is computationally more efficient than the existing RK method. A number of test problems are solved and the numerical results compared with the existing RK method are given. |
| first_indexed | 2025-11-15T10:51:44Z |
| format | Conference or Workshop Item |
| id | upm-57196 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:51:44Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-571962017-09-08T10:34:19Z http://psasir.upm.edu.my/id/eprint/57196/ Fourth order 4-stages improved Runge-Kutta method with minimized error norm Rabiei, Faranak Ismail, Fudziah In this paper the improved Runge-Kutta method of order four with 4-stages for solving first order ordinary differential equation is proposed. The method is based on classical Runge-Kutta (RK) method also can be considered as special class of two-step method. Here, the coefficients of the method are obtained using the minimization of the error norm up to order five. The improved method with only 4-stages is more accurate than fourth order 4-stages RK method. Therefore it is computationally more efficient than the existing RK method. A number of test problems are solved and the numerical results compared with the existing RK method are given. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57196/1/Fourth%20order%204-stages%20improved%20Runge-Kutta%20method%20with%20minimized%20error%20norm.pdf Rabiei, Faranak and Ismail, Fudziah (2013) Fourth order 4-stages improved Runge-Kutta method with minimized error norm. In: Statistics and Operational Research International Conference (SORIC 2013), 3–5 Dec. 2013, Sarawak, Malaysia. (pp. 153-158). 10.1063/1.4894341 |
| spellingShingle | Rabiei, Faranak Ismail, Fudziah Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title | Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title_full | Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title_fullStr | Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title_full_unstemmed | Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title_short | Fourth order 4-stages improved Runge-Kutta method with minimized error norm |
| title_sort | fourth order 4-stages improved runge-kutta method with minimized error norm |
| url | http://psasir.upm.edu.my/id/eprint/57196/ http://psasir.upm.edu.my/id/eprint/57196/ http://psasir.upm.edu.my/id/eprint/57196/1/Fourth%20order%204-stages%20improved%20Runge-Kutta%20method%20with%20minimized%20error%20norm.pdf |