Energy preserving integration of bi-Hamiltonian partial differential equations

KARASÖZEN B., Simsek G.

APPLIED MATHEMATICS LETTERS, vol.26, no.12, pp.1125-1133, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 12
  • Publication Date: 2013
  • Doi Number: 10.1016/j.aml.2013.06.005
  • Journal Name: APPLIED MATHEMATICS LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1125-1133
  • Keywords: Energy preservation, Bi-Hamiltonian systems, Poisson structure, Korteweg de Vries equation, Dispersion, POISSON INTEGRATORS
  • Middle East Technical University Affiliated: Yes

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.