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Geometric numerical integrators for Hunter–Saxton-like equations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-6490-1957
2017 (English)In: Japan journal of industrial and applied mathematics, ISSN 0916-7005, E-ISSN 1868-937X, Vol. 34, no 2, 441-472 p.Article in journal (Refereed) Published
Abstract [en]

We present novel geometric numerical integrators for Hunter-Saxton-like equations by means of new multi-symplectic formulations and known Hamiltonian structures of the problems. We consider the Hunter-Saxton equation, the modified Hunter-Saxton equation, and the two-component Hunter-Saxton equation. Multi-symplectic discretisations based on these new formulations of the problems are exemplified by means of the explicit Euler box scheme, and Hamiltonian-preserving discretisations are exemplified by means of the discrete variational derivative method. We explain and justify the correct treatment of boundary conditions in a unified manner. This is necessary for a proper numerical implementation of these equations and was never explicitly clarified in the literature before, to the best of our knowledge. Finally, numerical experiments demonstrate the favourable behaviour of the proposed numerical integrators.

Place, publisher, year, edition, pages
2017. Vol. 34, no 2, 441-472 p.
Keyword [en]
Hunter-Saxton equation; Modified Hunter-Saxton equation; Two-component Hunter-Saxton equation; Multi-symplectic formulation; Numerical discretisation; Geometric numerical integration; Discrete variational derivative method; Multi-symplectic schemes; Euler box scheme
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-137245DOI: 10.1007/s13160-017-0252-1ISI: 000406362100007OAI: oai:DiVA.org:umu-137245DiVA: diva2:1117097
Funder
The Royal Swedish Academy of Sciences, FY2012
Available from: 2017-06-28 Created: 2017-06-28 Last updated: 2017-08-24Bibliographically approved

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Citation style
  • apa
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  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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