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

Hairer, E (Geneve)
Tuesday 27 March 2007, 09:45-10:30

Seminar Room 1, Newton Institute


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.


[pdf ]




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