论文信息 - Note on derivation of order conditions for ARKN methods for perturbed oscillators

Note on derivation of order conditions for ARKN methods for perturbed oscillators

Abstract J.M. Franco derived the sufficient order conditions as well as the necessary and sufficient order conditions for his Adapted Runge–Kutta–Nystrom methods (in short notation ARKN methods) based on the B-series theory [J.M. Franco, Runge–Kutta–Nystrom methods adapted to the numerical integration of perturbed oscillators, Comput. Phys. Comm. 147 (2002) 770–787]. Unfortunately, some fundamental mistakes have been made in the derivation of order conditions in that paper. In view of importance of the algebraic order theory for ARKN methods, a new and correct derivation of the order conditions for the ARKN methods is presented in this short note.

[1] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[2] Hans Van de Vyver,et al. Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems , 2005, Comput. Phys. Commun..

[3] J. M. Franco. New methods for oscillatory systems based on ARKN methods , 2006 .

[4] J. M. Franco. A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators , 2003 .

[5] Xinyuan Wu,et al. A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators , 2007 .

[6] J. M. Franco. Runge–Kutta–Nyström methods adapted to the numerical integration of perturbed oscillators , 2002 .

[7] E. Hairer,et al. Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .