A new diagonally implicit Runge-Kutta-Nystrom method for periodic IVPs - Senu, Norazak; Suleiman, Mohamed; Ismail, Fudziah; Othman, Mohamed (World Scientific and Engineering Academy and Society (WSEAS) Press, 2010)
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.