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

Date: 
Tuesday 27th March 2007 - 09:45 to 10:30
Venue: 
INI Seminar Room 1
Session Chair: 
A Iserles
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons