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Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
Department of Mathematical Sciences, NTNU.ORCID iD: 0000-0001-6490-1957
Section de Mathématiques, Université de Genève.
Mathematisches Institut, Universität Tübingen.
2008 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 110, no 2, 113-143 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2008. Vol. 110, no 2, 113-143 p.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-59158DOI: 10.1007/s00211-008-0163-9ISI: 000257867700001OAI: oai:DiVA.org:umu-59158DiVA: diva2:551360
Available from: 2012-09-11 Created: 2012-09-10 Last updated: 2017-12-07Bibliographically approved

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