Efficient high-order time discretization methods for PDEs

May 8-10, 2019 - Villa Orlandi, Anacapri, Italy

Invited Lecture

Numerical long-time conservation of energy, momentum and actions for nonlinear wave equations

Ernst Hairer,

University of Geneva, Switzerland

Abstract

This talk considers nonlinearly perturbed wave equations, pseudo-spectral semi-discretizations and full discretizations using trigonometric time integrators. The long-time near-conservation of energy, momentum, and harmonic actions is studied. Rigorous statements are shown under suitable numerical non-resonance conditions and under a CFL condition. The time step is not assumed to be small compared to the inverse of the largest frequency in the space-discretized system, so that classical backward error analysis cannot be applied.
The proofs of the statements on the long-time conservation properties are based on the technique of modulated Fourier expansions.

This is joint work with Christian Lubich and David Cohen. Related publications (2008) can be downloaded from http://www.unige.ch/~hairer/preprints.html


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