Energy conservative stochastic difference scheme for stochastic Hamilton dynamical systems
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An energy conservative stochastic difference scheme is proposed for a one-dimensional stochastic Hamilton dynamical system governed by a stochastic differential equations in which the energy function,i.e. Hamiltonian, becomes a conserved quantity. The scheme is given by an stochastic extension of Greenspan’s scheme which leaves Hamiltonians numerically invariant for deterministic Hamilton dynamical systems. The local error of accuracy of numerical solutions derived from the stochastic difference scheme is investigated. An illustrative numerical experiment for the scheme to a simple stochastic Hamilton system is also given.
Key wordsstochastic difference scheme energy conservative scheme stochastic Hamilton dynamical systems
- L. Arnold, Stochastic Differential Equations: Theory and Applications. John Wiley & Sons, New York, 1973.Google Scholar
- J.M. Bismut, Mécanique Aléatoire. Lect. Notes in Math.,866, Springer, Berlin, 1981.Google Scholar
- Y. Ishimori, An energy conservative difference scheme of fourth order. Preprint (1997).Google Scholar
- G.N. Milstein, Numerical Integration of Stochastic Differential Equations. Kluwer, Dordrecht, 1995.Google Scholar