Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 231, Issue 20, Pages 6770-6789Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.06.022
Keywords
Average vector field method; Hamiltonian PDEs; Dissipative PDEs; Time integration
Funding
- Australian Research Council
- Marsden Fund of the Royal Society of New Zealand
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We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure, also preserves the correct monotonic decrease of energy. The method is illustrated by many examples. In the Hamiltonian case these include: the sine-Gordon, Korteweg-de Vries, nonlinear Schrodinger, (linear) time-dependent Schrodinger, and Maxwell equations. In the dissipative case the examples are: the Allen-Cahn, Cahn-Hilliard, Ginzburg-Landau, and heat equations. (C) 2012 Elsevier Inc. All rights reserved.
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