High-order Hamiltonian splitting for the Vlasov–Poisson equations
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Other documents of the author: Casas, Fernando; Crouseilles, Nicolas; Faou, Erwan; Mehrenberger, Michel
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
High-order Hamiltonian splitting for the Vlasov–Poisson equationsDate
2017Publisher
Springer VerlagISSN
0029-599X; 0945-3245Bibliographic citation
Casas, F., Crouseilles, N., Faou, E. et al. Numer. Math. (2017) 135: 769. doi:10.1007/s00211-016-0816-zType
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007/s00211-016-0816-zVersion
info:eu-repo/semantics/acceptedVersionAbstract
We consider the Vlasov–Poisson equation in a Hamiltonian
framework and derive new time splitting methods based on the
decomposition of the Hamiltonian functional between the kinetic and
electric energy. Assuming ... [+]
We consider the Vlasov–Poisson equation in a Hamiltonian
framework and derive new time splitting methods based on the
decomposition of the Hamiltonian functional between the kinetic and
electric energy. Assuming smoothness of the solutions, we study the
order conditions of such methods. It appears that these conditions are
of Runge–Kutta–Nystr¨om type. In the one dimensional case, the order
conditions can be further simplified, and efficient methods of order 6
with a reduced number of stages can be constructed. In the general
case, high-order methods can also be constructed using explicit computations
of commutators. Numerical results are performed and show
the benefit of using high-order splitting schemes in that context. Complete
and self-contained proofs of convergence results and rigorous error
estimates are also given. [-]
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Numer. Math. (2017) 135:769–801Rights
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