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

Abstract

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.

References in corpus (4)

• Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems
• Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
• Energy separation in oscillatory Hamiltonian systems without any non-resonance condition
• Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequency