An Isaac Newton Institute Workshop

The Theory of Highly Oscillatory Problems

Conservation of energy and actions in numerical discretizations of nonlinear wave equations

Author: Ernst Hairer (University of Geneva)

Abstract

For numerical discretizations of nonlinearly perturbed wave equations the long-time near-conservation of energy, momentum, and harmonic actions is studied. The proofs are based on the technique of modulated Fourier expansions in time. Rigorous statements on the long-time conservation properties are shown under suitable numerical non-resonance conditions and under a CFL condition. The time step need not be small compared to the inverse of the largest frequency in the space-discretized system.

This is joint work with Christian Lubich and David Cohen.