A robust trigonometrically fitted embedded pair for perturbed oscillators

Authors:
Yonglei Fang;Yongzhong Song;Xinyuan Wu
Affiliations:
School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, PR China;School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, PR China;State Key Laboratory for Novel Software Technology at Nanjing University, PR China and Department of Mathematics, Nanjing University, Nanjing 210093, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

A new kind of trigonometrically fitted embedded pair of explicit ARKN methods for the numerical integration of perturbed oscillators is presented in this paper. This new pair is based on the trigonometrically fitted ARKN method of order five derived by Yang and Wu in [H.L. Yang, X.Y. Wu, Trigonometrically-fitted ARKN methods for perturbed oscillators, Appl. Numer. Math. 9 (2008) 1375-1395]. We analyze the stability properties, phase-lag (dispersion) and dissipation of the higher-order method of the new pair. Numerical experiments carried out show that our new embedded pair is very competitive in comparison with the embedded pairs proposed in the scientific literature.