Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y')

Citation

Salama, Tahani Mohamed and Senu, Norazak and Ibrahim, Zarina Bibi and Nik Long, Nik Mohd Asri (2018) Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y'). Discrete Dynamics in Nature and Society, 2018. art. no. 2393015. pp. 1-10. ISSN 1026-0226; ESSN: 1607-887X

Abstract

This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form y'' (x) = f (x,y, y') including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods.

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Additional Metadata

Item Type:	Article
Divisions:	Faculty of Science Institute for Mathematical Research
DOI Number:	https://doi.org/10.1155/2018/2393015
Publisher:	Hindawi
Keywords:	Runge-Kutta-Nyström; Second derivative; Third derivative; Differential equations
Depositing User:	Nurul Ainie Mokhtar
Date Deposited:	22 Oct 2020 11:06
Last Modified:	22 Oct 2020 11:06
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2018/2393015
URI:	http://psasir.upm.edu.my/id/eprint/72537
Statistic Details:	View Download Statistic

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