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Energy preserving integration of bi-Hamiltonian partial differential equations
Date
2013-12-01
Author
Karasözen, Bülent
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The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to examine the nonlinear dynamics after discretization.
Subject Keywords
Energy preservation
,
Bi-Hamiltonian systems
,
Poisson structure
,
Korteweg de vries equation
,
Dispersion
URI
https://hdl.handle.net/11511/30940
Journal
APPLIED MATHEMATICS LETTERS
DOI
https://doi.org/10.1016/j.aml.2013.06.005
Collections
Graduate School of Applied Mathematics, Article
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B. Karasözen, “Energy preserving integration of bi-Hamiltonian partial differential equations,”
APPLIED MATHEMATICS LETTERS
, pp. 1125–1133, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30940.