Long-term analysis of exponential integrators for highly oscillatory conservative systems
Provides theoretical guarantees for numerical methods used in simulating oscillatory systems, which is important for computational physics and engineering.
The paper analyzes long-term energy and kinetic energy conservation of exponential integrators for highly oscillatory conservative systems, deriving almost-invariants from modulated Fourier expansions and confirming results numerically.
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.