Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y ′ ′ ( x ) = f ( x , y , y ′ )
Joint Authors
Asri Nik Long, Nik Mohd
Senu, Norazak
Mohamed, T. S.
Ibrahim, Z. B.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-20
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Mohamed, T. S.& Senu, Norazak& Ibrahim, Z. B.& Asri Nik Long, Nik Mohd. 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،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152389
Modern Language Association (MLA)
Mohamed, T. S.…[et al.]. 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 No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1152389
American Medical Association (AMA)
Mohamed, T. S.& Senu, Norazak& Ibrahim, Z. B.& Asri Nik Long, Nik Mohd. 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. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152389
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152389