A three-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is developed for the numerical integration of special second-order ordinary differential equations. Algebraic order conditions of the method are obtained and fourth-order method is derived. The second-order initial value problems of ordinary differential equations (ODEs) are solved directly using TSRKN and Runge-Kutta-Nyström (RKN) methods. The problems were then reduced to first-order system when solved by Runge-Kutta (RK) method. Numerical comparison of this new method with the existing RK and RKN methods of the same order using constant step size are carried out to illustrate its efficiency and it shows that the new method has clear advantage in terms of function evaluation.
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22 April 2013
PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation
18–20 December 2012
Palm Garden Hotel, Putrajaya, Malaysia
Research Article|
April 22 2013
A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations
Latifah Md Ariffin;
Latifah Md Ariffin
Department of Mathematics and Statistics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor DT,
Malaysia
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Norazak Senu;
Norazak Senu
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor DE,
Malaysia
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Mohamed Suleiman
Mohamed Suleiman
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor DE,
Malaysia
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AIP Conf. Proc. 1522, 323–329 (2013)
Citation
Latifah Md Ariffin, Norazak Senu, Mohamed Suleiman; A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations. AIP Conf. Proc. 22 April 2013; 1522 (1): 323–329. https://doi.org/10.1063/1.4801142
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