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Fifth order Runge-Kutta-Nyström methods for solving linear second order oscillatory problems


Salih, Mohammed M. and Ismail, Fudziah and Senu, Norazak (2016) Fifth order Runge-Kutta-Nyström methods for solving linear second order oscillatory problems. Far East Journal of Applied Mathematics, 95 (2). pp. 141-156. ISSN 0972-0960


In this paper, order conditions for Runge-Kutta-Nyström (RKN) method for solving second order linear ordinary differential equations (LODEs) are derived up to order six. Based on the order conditions, a new fifth order four-stage RKN method which is specially designed for the integration of second order linear ordinary differential equations (LODEs) is constructed with first same as last (FSAL) property. Then we phase-fitted the method such that it has zero phase-lag and zero dissipation. Phase-lag or dispersion error is the angle between the true and the approximated solutions, whereas dissipation is the distance of the computed solution from the standard cyclic solution. A set of test problems are used to validate the method and numerical results show that the phase-fitted method produced smaller global error compared to the original method as well as other existing RKN method in the scientific literature.

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Additional Metadata

Item Type: Article
Subject: Runge-Kutta-Nyström; Phase-fitted; Oscillatory; Linear ODEs
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.17654/AM095020141
Publisher: Pushpa Publishing House
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 13 Mar 2018 04:15
Last Modified: 13 Mar 2018 04:15
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.17654/AM095020141
URI: http://psasir.upm.edu.my/id/eprint/54314
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