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Geometric numerical...
Geometric numerical integrators for Hunter–Saxton-like equations
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- Miyatake, Yuto (författare)
- Nagoya University
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- Cohen, David (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,University of Innsbruck,Umeå University
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- Furihata, Daisuke (författare)
- Osaka University
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- Matsuo, Takayasu (författare)
- University of Tokyo, Japan
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(creator_code:org_t)
- 2017-06-12
- 2017
- Engelska.
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Ingår i: Japan journal of industrial and applied mathematics. - : Springer Science and Business Media LLC. - 0916-7005 .- 1868-937X. ; 34:2, s. 441-472
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- 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
Publikations- och innehållstyp
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- art (ämneskategori)
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