Trigonometrically-fitted ARKN methods for perturbed oscillators

Authors:
Hongli Yang;Xinyuan Wu
Affiliations:
State Key Laboratory for Novel Software Technology at Nanjing University, Department of Mathematics, Nanjing University, Nanjing 210093, PR China;State Key Laboratory for Novel Software Technology at Nanjing University, Department of Mathematics, Nanjing University, Nanjing 210093, PR China
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

In this paper, new and robust trigonometrically-fitted adapted Runge-Kutta-Nystrom methods for the numerical integration of perturbed oscillators are presented, which combine the features of trigonometrically-fitted methods with ARKN methods. Based on the linear-operator theory, the necessary and sufficient order conditions for these methods are derived. The numerical experiments are accompanied to show the efficiency and competence of our methods in comparison with some well-known methods.