Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′)
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. I...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/2393015 |
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| _version_ | 1832552164887625728 |
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| author | T. S. Mohamed N. Senu Z. B. Ibrahim N. M. A. Nik Long |
| author_facet | T. S. Mohamed N. Senu Z. B. Ibrahim N. M. A. Nik Long |
| author_sort | T. S. Mohamed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7318c916443242f7be3ba03d45736a68 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-7318c916443242f7be3ba03d45736a682025-02-03T05:59:20ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/23930152393015Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′)T. S. Mohamed0N. Senu1Z. B. Ibrahim2N. M. A. Nik Long3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaThis 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.http://dx.doi.org/10.1155/2018/2393015 |
| spellingShingle | T. S. Mohamed N. Senu Z. B. Ibrahim N. M. A. Nik Long 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 |
| title | Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′) |
| title_full | Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′) |
| title_fullStr | Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′) |
| title_full_unstemmed | Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′) |
| title_short | Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations y′′(x)=f(x,y,y′) |
| title_sort | efficient two derivative runge kutta nystrom methods for solving general second order ordinary differential equations y x f x y y |
| url | http://dx.doi.org/10.1155/2018/2393015 |
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