A new numerical method for the integration of highly oscillatory second-order ordinary differential equations (Q1308560)

This paper presents a new discretization scheme for the efficient integration of highly oscillatory second-order ordinary differential equations. The discretization scheme is based on the principle of coherence proposed by \textit{J. Hersch} [Numer. Math. Differ.-Gleichg. funktionalanal. Hilfsm. Tagungen Clausthal-Zellerfeld und Oberwolfach 1972, ISNM 19, 121-124 (1974; Zbl 0293.65066)]. The analysis of the formulas reveals properties such as absolute stability and \(P\)-stability which indicate the ability of the method to handle highly oscillatory differential equations. This is confirmed by numerical results.