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New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems


Citation

Moo, Kwong Wing and Senu, Norazak and Ismail, Fudziah and Suleiman, Mohamed (2013) New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems. Abstract and Applied Analysis, 2013. art. no. 939367. pp. 1-9. ISSN 1085-3375; ESSN: 1687-0409

Abstract

Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. Firstly, a three-stage fourth-order Garcia’s RKN method. Another method is Hairer’s RKN method of four-stage fifth-order. Both new derived methods have two variable coefficients with phase-lag of order infinity and zero amplification error (zero dissipative). Numerical tests are performed and the results show that the new methods are more accurate than the other methods in the literature.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2013/939367
Publisher: Hindawi Publishing Corporation
Keywords: Runge-Kutta-Nystrom method; Numerical comparison; Runge-Kutta; Differential equation
Depositing User: Umikalthom Abdullah
Date Deposited: 01 Jul 2014 07:24
Last Modified: 20 Oct 2017 04:14
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/939367
URI: http://psasir.upm.edu.my/id/eprint/30120
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