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• W2085347462 abstract "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 Schrödinger, (linear) time-dependent Schrödinger, and Maxwell equations. In the dissipative case the examples are: the Allen–Cahn, Cahn–Hilliard, Ginzburg–Landau, and heat equations." @default.
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• W2085347462 date "2012-08-01" @default.
• W2085347462 modified "2023-10-18" @default.
• W2085347462 title "Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method" @default.
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• W2085347462 doi "https://doi.org/10.1016/j.jcp.2012.06.022" @default.
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