Abstract

This talk is to present structure-preserving algorithms for oscillatory problems that arise in a wide range of fields such as astronomy, molecular dynamics, classical mechanics, quantum mechanics, chemistry, biology and engineering. Such problems can often be modelled by initial value problems of second-order differential equations with a linear term characterizing the oscillatory structure of the systems. Since general-purpose high order Runge-Kutta (RK) methods, Runge-Kutta-Nystr\”om (RKN) methods, and linear multistep methods (LMM) cannot respect the special structures of oscillatory problems in long-term integration, innovative integrators have to be designed. This talk will pay attention to both theories and methods for solving second-order differential equations with oscillatory solutions.