Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems

In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.

Automated summary

In this paper, the long-time numerical conservation of energy and kinetic energy for highly oscillatory conservative systems is investigated using widely used exponential integrators. Modulated Fourier expansions of two types of exponential integrators are constructed, and the long-time numerical conservation of energy and kinetic energy is obtained by deriving two almost-invariants of the expansions. Practical examples and numerical experiments confirm and demonstrate the theoretical results.