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Long-term analysis of exponential integrators for highly oscillatory conservative systems

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arxiv 1809.07268 v1 pith:OI47M24D submitted 2018-09-19 math.NA cs.NA

Bin Wang , Jiyong Li , Yonglei Fang This is my paper · ORCID
classification math.NAcs.NA
keywords energyexponentialintegratorsconservativeexpansionshighlykineticlong-time
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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.

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