Poisson integrators for Volterra lattice equations
T. Ergenç, B. Karasözen
Abstract
The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm preservation of the corresponding Hamiltonians, Casimirs, quadratic and cubic integrals in the long-term with different orders of accuracy.
Create a lesson
Related papers
To lift or not to lift: Operator inference for nonlinear PDEs with boundary control
Zhuoyuan Wang, Yorie Nakahira, Wael H. Ali et al.
Sobolev--Poincaré inequalities for piecewise W2,p functions over general polytopic meshes
Michele Botti, Lorenzo Mascotto
Robust Multigrid on Adaptive Meshes for the Integral Fractional Laplacian
Markus Faustmann, Paula Hilbert, Ani Miraçi et al.
A Tensor-Network Chebyshev--Galerkin Method for Boundary-Value Problems in Computational Mechanics
Juan José Rodríguez-Aldavero, Ángel de la Rosa Velasco, Juan José García-Ripoll
A volume-conserving ALE continuous Galerkin method with residual-based Dirichlet--Neumann fluxes for nonlinear free-surface waves
Fan Wang, Yinhua Xia, Yan Xu
A weak Galerkin finite element method for the coupled Stokess-Biot problem
Rui Li, Hui Peng, Xiuli Wang