An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems

A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost...

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Main Authors: Senu, Norazak, Suleiman, Mohamed, Ismail, Fudziah
Format: Article
Published: Institute of Physics Publishing 2009
Online Access:http://psasir.upm.edu.my/id/eprint/13027/
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author Senu, Norazak
Suleiman, Mohamed
Ismail, Fudziah
author_facet Senu, Norazak
Suleiman, Mohamed
Ismail, Fudziah
author_sort Senu, Norazak
building UPM Institutional Repository
collection Online Access
description A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost for this pair is four function evaluations at each step of integration. Numerical comparisons with several codes in the scientific literature such as RKN5(4)D, RKN5(4)B,RKN4(3)G and DOPRI5 show the efficiency of the new method developed.
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institution Universiti Putra Malaysia
institution_category Local University
last_indexed 2025-11-15T07:52:09Z
publishDate 2009
publisher Institute of Physics Publishing
recordtype eprints
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spelling upm-130272015-07-29T07:37:58Z http://psasir.upm.edu.my/id/eprint/13027/ An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems Senu, Norazak Suleiman, Mohamed Ismail, Fudziah A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost for this pair is four function evaluations at each step of integration. Numerical comparisons with several codes in the scientific literature such as RKN5(4)D, RKN5(4)B,RKN4(3)G and DOPRI5 show the efficiency of the new method developed. Institute of Physics Publishing 2009-07 Article PeerReviewed Senu, Norazak and Suleiman, Mohamed and Ismail, Fudziah (2009) An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems. Physica Scripta, 80 (1). art. no. 015005. pp. 1-7. ISSN 0031-8949; ESSN: 1402-4896 http://iopscience.iop.org/1402-4896/80/1/015005 10.1088/0031-8949/80/01/015005
spellingShingle Senu, Norazak
Suleiman, Mohamed
Ismail, Fudziah
An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title_full An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title_fullStr An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title_full_unstemmed An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title_short An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
title_sort embedded explicit runge-kutta-nystrom method for solving oscillatory problems
url http://psasir.upm.edu.my/id/eprint/13027/
http://psasir.upm.edu.my/id/eprint/13027/
http://psasir.upm.edu.my/id/eprint/13027/