Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

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Reference

Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

COHEN, David, HAIRER, Ernst, LUBICH, Christian

Abstract

For classes of symplectic and symmetric time-stepping methods - trigonometric integrators and the Stšrmer-Verlet or leapfrog method - applied to spectral semi-discretizations of semilinear wave equations in a weakly nonlinear setting, it is shown that energy, momentum, and all harmonic actions are approximately preserved over long times. For the case of interest where the CFL number is not a small parameter, such results are outside the reach of standard backward error analysis. Here, they are instead obtained via a modulated Fourier expansion in time.

COHEN, David, HAIRER, Ernst, LUBICH, Christian. Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Numerische Mathematik , 2008, vol. 110, p. 113-143

DOI : 10.1007/s00211-008-0163-9

Available at:

http://archive-ouverte.unige.ch/unige:5202

Disclaimer: layout of this document may differ from the published version.

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