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Numerical methods for Hamiltonian PDEs

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Thomas J Bridges1 and Sebastian Reich2

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The paper provides an introduction and survey of conservative discretization methods for Hamiltonian partial differential equations. The emphasis is on variational, symplectic and multi-symplectic methods. The derivation of methods as well as some of their fundamental geometric properties are discussed. Basic principles are illustrated by means of examples from wave and fluid dynamics.


PACS

45.20.Jj Lagrangian and Hamiltonian mechanics

02.60.Lj Ordinary and partial differential equations; boundary value problems

45.20.dh Energy conservation

45.10.Na Geometrical and tensorial methods

45.20.df Momentum conservation

MSC

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

65L05 Initial value problems

70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction

70G75 Variational methods

Subjects

Mathematical physics

Computational physics

Dates

Issue 19 (12 May 2006)

Received 13 September 2005, in final form 14 February 2006

Published 24 April 2006



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