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Energy preserving integration of bi-Hamiltonian partial differential equations |
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| Authors: | Bülent Karasözen Görkem Şimşek |
| Institution: | 1. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey;2. Multiscale Engineering Fluid Dynamics, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
| Abstract: | 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. |
| Keywords: | Energy preservation Bi-Hamiltonian systems Poisson structure Korteweg de Vries equation Dispersion |
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