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Math. Comput. Appl. 2016, 21(4), 46; doi:10.3390/mca21040046

A 5(4) Embedded Pair of Explicit Trigonometrically-Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of Oscillatory Initial Value Problems

1,2,†
,
1,†
and
2,*
1
Department of Mathematics, Universiti Putra Malaysia, Serdang 43400, Malaysia
2
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Li-Qun Chen
Received: 6 June 2016 / Revised: 28 September 2016 / Accepted: 8 November 2016 / Published: 17 November 2016
Download PDF [807 KB, uploaded 17 November 2016]

Abstract

A 5(4) pair of embedded explicit trigonometrically-fitted Runge–Kutta–Nyström (EETFRKN) methods especially designed for the numerical integration of second order initial value problems with oscillatory solutions is presented in this paper. Algebraic order analysis and the interval of absolute stability for the new method are also discussed. The new method is capable of integrating the test equation y = w 2 y . The new method is much more efficient than the other existing Runge–Kutta and Runge–Kutta–Nyström methods.
Keywords: trigonometric fitting; Runge–Kutta–Nyström method; oscillatory initial value problems trigonometric fitting; Runge–Kutta–Nyström method; oscillatory initial value problems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Demba, M.A.; Senu, N.; Ismail, F. A 5(4) Embedded Pair of Explicit Trigonometrically-Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of Oscillatory Initial Value Problems. Math. Comput. Appl. 2016, 21, 46.

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