A new diagonally implicit Runge-Kutta-Nyström method for periodic IVPs

Authors:
Norazak Senu;Mohamed Suleiman;Fudziah Ismail;Mohamed Othman
Affiliations:
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia;Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia;Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia;Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia
Venue:
WSEAS Transactions on Mathematics
Year:
2010

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Abstract

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-order with dispersive order six and 'small' principal local truncation error terms and dissipation constant. The analysis of phase-lag, dissipation and stability of the method are also given. This new method is more efficient when compared with current methods of similar type for the numerical integration of second-order differential equations with periodic solutions, using constant step size.