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

Abstract

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 Hersch. 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.