ENERGY PRESERVING METHODS FOR VOLTERRA LATTICE EQUATION

Year 2011, Volume: 01 Issue: 2, 192 - 202, 01.12.2011

Bulent Karasozen Ozge Erdem

Abstract

We investigate linear energy preserving methods for the Volterra lattice equation as non-canonical Hamiltonian system. The averaged vector field method was applied to the Volterra lattice equation in bi-Hamiltonian form with quadratic and cubic Poisson brackets. Numerical results confirm the excellent long time preservation of the Hamiltonians and the polynomial integrals.

Keywords

Energy preserving integrators, Runge-Kutta methods, Bi-Hamiltonian systems, Poisson structure

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