Energy preserving integration of bi-Hamiltonian partial differential equations

B. Karasozen; G. Simsek

doi:10.1016/j.aml.2013.06.005

Energy preserving integration of bi-Hamiltonian partial differential equations

B. Karasozen, G. Simsek

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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. (c) 2013 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1125-1133
Journal	Applied Mathematics Letters
Volume	26
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2013.06.005
Publication status	Published - 2013

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title = "Energy preserving integration of bi-Hamiltonian partial differential equations",

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. (c) 2013 Elsevier Ltd. All rights reserved.",

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AU - Karasozen, B.

AU - Simsek, G.

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N2 - 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. (c) 2013 Elsevier Ltd. All rights reserved.

AB - 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. (c) 2013 Elsevier Ltd. All rights reserved.

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DO - 10.1016/j.aml.2013.06.005

M3 - Article

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VL - 26

SP - 1125

EP - 1133

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

Energy preserving integration of bi-Hamiltonian partial differential equations

Abstract

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