Poisson integrators for Volterra lattice equations. (English) Zbl 1110.65115
This paper deals with the solution of Volterra lattice equations. It is shown that the symplectic Euler method preserves the quadratic Poisson structure of the periodic Volterra lattice. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm long-term preservation of the Hamiltonian, Casimirs and the first integrals.
Reviewer: Rudolf Scherer (Karlsruhe)
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
Korteweg-de Vries equation; bi-Hamiltonian systems; Poisson structure; symplectic Euler method; Lobatto IIIA-B methods; numerical resultsReferences:
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