jaem

TWMS Journal of Applied and Engineering Mathematics

2146-1147 2587-1013

Işık University Press

ENERGY PRESERVING INTEGRATION OF BI-HAMILTONIAN PARTIAL DIFFERENTIAL EQUATIONS

Karasozen

Bulent

Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey Simsek

Gorkem

Multiscale Engineering Fluid Dynamics, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

06 01 2013

3 1 75 86

2010

TWMS Journal of Applied and Engineering Mathematics

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 discreization.

Energy preservation bi-Hamiltonian systems Poisson structure KdV equation

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