منابع مشابه
Poisson integrators
An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems and the discrete...
متن کاملLinear energy-preserving integrators for Poisson systems
For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge–Kutta method with ...
متن کاملEnergy-preserving integrators for stochastic Poisson systems
A new class of energy-preserving numerical schemes for stochastic Hamiltonian systems with non-canonical structure matrix (in the Stratonovich sense) is proposed. These numerical integrators are of mean-square order one and also preserve quadratic Casimir functions. In the deterministic setting, our schemes reduce to methods proposed in [9] and [6].
متن کاملLie-Poisson integrators: A Hamiltonian, variational approach
In this paper we present a systematic and general method for developing variational integrators for LiePoisson Hamiltonian systems living in a finite-dimensional space g∗, the dual of Lie algebra associated with a Lie group G . These integrators are essentially different discretized versions of the Lie-Poisson variational principle, or a modified Lie-Poisson variational principle proposed in th...
متن کاملA derivation of energy-preserving exponentially-fitted integrators for Poisson systems
Exponentially-fitted (EF) methods are special methods for ordinary differential equations that better catch periodic/oscillatory solutions. Such solutions often appear in Hamiltonian systems, and in view of this, symplectic or energy-preserving variants of EF methods have been intensively studied recently. In these studies, the symplectic variants have been further applied to Poisson systems, w...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2004
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2005.01.015