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Zbl 1090.65138
Bridges, Thomas J.; Reich, Sebastian
Numerical methods for Hamiltonian PDEs.
(English)
[J] J. Phys. A, Math. Gen. 39, No. 19, 5287-5320 (2006). ISSN 0305-4470

Summary: 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.
MSC 2000:
*65P10 Hamiltonian systems including symplectic integrators
37M15 Symplectic integrators
37K05 Hamiltonian structures, etc.

Keywords: variational methods; numerical examples; Hamiltonian partial differential equations; multi-symplectic methods

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Scientific prize winners of the ICM 2010
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Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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