ENERGY PRESERVING METHODS FOR VOLTERRA LATTICE EQUATION

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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