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

Cohen, David and Hairer, Ernst and Lubich, Christian. (2008) Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Numerische Mathematik, Vol. 110, H. 2. pp. 113-143.

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Official URL: http://edoc.unibas.ch/dok/A5248812

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Abstract

For classes of symplectic and symmetric time-stepping methods- trigonometric integrators and the Stormer-Verlet or leapfrog method-applied to spectral semi-discretizations of semilinear wave equations in a weakly non-linear 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Numerik (Cohen)
UniBasel Contributors:Cohen, David
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Springer
ISSN:0029-599X
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:22 Mar 2012 14:27
Deposited On:22 Mar 2012 13:58

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