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

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Lubich, Christian
Published in Numerische Mathematik. 2008, vol. 110, p. 113-143
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.
Keywords Nonlinear wave equationConservation of energyMomentum and actionsLong-time behaviourTrigonometric methodsLeapfrogStšrmer-Verlet method
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COHEN, David, HAIRER, Ernst, LUBICH, Christian. Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. In: Numerische Mathematik, 2008, vol. 110, p. 113-143. https://archive-ouverte.unige.ch/unige:5202

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Deposited on : 2010-02-16

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