Volume 38, Issue 5
On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations

Ludwig Gauckler

J. Comp. Math., 38 (2020), pp. 705-714.

Published online: 2020-04

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  • Abstract

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.

  • Keywords

Oscillatory Hamiltonian systems, Trigonometric integrators, Energy conservation, Long-time behaviour, Modified energy.

  • AMS Subject Headings

65P10, 65L05, 37M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ludwig.gauckler.math@gmail.com (Ludwig Gauckler)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-705, author = {Gauckler , Ludwig }, title = {On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {5}, pages = {705--714}, abstract = {

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1903-m2018-0090}, url = {http://global-sci.org/intro/article_detail/jcm/16665.html} }
TY - JOUR T1 - On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations AU - Gauckler , Ludwig JO - Journal of Computational Mathematics VL - 5 SP - 705 EP - 714 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1903-m2018-0090 UR - https://global-sci.org/intro/article_detail/jcm/16665.html KW - Oscillatory Hamiltonian systems, Trigonometric integrators, Energy conservation, Long-time behaviour, Modified energy. AB -

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.

Ludwig Gauckler. (2020). On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations. Journal of Computational Mathematics. 38 (5). 705-714. doi:10.4208/jcm.1903-m2018-0090
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