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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Citation Formats

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.