Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs
In this paper, the First Same As Last (FSAL) technique is implemented to Two Derivative Runge-Kutta method (TDRK) for the numerical integration of first order Initial Value Problems (IVPs). Using the FSAL property, a four stages fifth algebraic order TDRK method is constructed. Hence, the new method...
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| Format: | Article |
| Language: | English |
| Published: |
International Association of Research and Science
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51872/ http://psasir.upm.edu.my/id/eprint/51872/1/Fifth%20order%20two%20derivative%20Runge-Kutta%20method%20with%20reduced%20function%20evaluations%20for%20solving%20IVPs.pdf |
| _version_ | 1848851951195783168 |
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| author | Senu, Norazak Ahmad, Nur Amirah Bachok @ Lati, Norfifah |
| author_facet | Senu, Norazak Ahmad, Nur Amirah Bachok @ Lati, Norfifah |
| author_sort | Senu, Norazak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the First Same As Last (FSAL) technique is implemented to Two Derivative Runge-Kutta method (TDRK) for the numerical integration of first order Initial Value Problems (IVPs). Using the FSAL property, a four stages fifth algebraic order TDRK method is constructed. Hence, the new method has three effective stages meaning that it has three function evaluations per step. It has two stages less compared with the classical Runge-Kutta for the same order. The stability of the method derived is analyzed. The numerical experiments are carried out to show the accuracy and efficiency of the method by comparing the derived method with other existing Runge-Kutta methods (RK). |
| first_indexed | 2025-11-15T10:30:20Z |
| format | Article |
| id | upm-51872 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:20Z |
| publishDate | 2016 |
| publisher | International Association of Research and Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-518722017-05-02T08:06:01Z http://psasir.upm.edu.my/id/eprint/51872/ Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs Senu, Norazak Ahmad, Nur Amirah Bachok @ Lati, Norfifah In this paper, the First Same As Last (FSAL) technique is implemented to Two Derivative Runge-Kutta method (TDRK) for the numerical integration of first order Initial Value Problems (IVPs). Using the FSAL property, a four stages fifth algebraic order TDRK method is constructed. Hence, the new method has three effective stages meaning that it has three function evaluations per step. It has two stages less compared with the classical Runge-Kutta for the same order. The stability of the method derived is analyzed. The numerical experiments are carried out to show the accuracy and efficiency of the method by comparing the derived method with other existing Runge-Kutta methods (RK). International Association of Research and Science 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51872/1/Fifth%20order%20two%20derivative%20Runge-Kutta%20method%20with%20reduced%20function%20evaluations%20for%20solving%20IVPs.pdf Senu, Norazak and Ahmad, Nur Amirah and Bachok @ Lati, Norfifah (2016) Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs. International Journal of Mathematical and Computational Methods, 1. pp. 421-428. ISSN 2367-895X http://www.iaras.org/iaras/journals/caijmcm/fifth-order-two-derivative-runge-kuttamethod-with-reduced-function-evaluations-for-solving-ivps |
| spellingShingle | Senu, Norazak Ahmad, Nur Amirah Bachok @ Lati, Norfifah Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title | Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title_full | Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title_fullStr | Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title_full_unstemmed | Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title_short | Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs |
| title_sort | fifth order two derivative runge-kutta method with reduced function evaluations for solving ivps |
| url | http://psasir.upm.edu.my/id/eprint/51872/ http://psasir.upm.edu.my/id/eprint/51872/ http://psasir.upm.edu.my/id/eprint/51872/1/Fifth%20order%20two%20derivative%20Runge-Kutta%20method%20with%20reduced%20function%20evaluations%20for%20solving%20IVPs.pdf |