Numerical Methods for Stochastic Systems Preserving Symplectic Structure
- 1 January 2002
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 40 (4), 1583-1604
- https://doi.org/10.1137/s0036142901395588
Abstract
Stochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are needed. A new class of fully implicit methods for stochastic systems is proposed. Increments of Wiener processes in these fully implicit schemes are substituted by some truncated random variables. A number of symplectic integrators is constructed. Special attention is paid to systems with separable Hamiltonians. Some results of numerical experiments are presented. They demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones.Keywords
This publication has 10 references indexed in Scilit:
- Symplectic Integration of Hamiltonian Systems with Additive NoiseSIAM Journal on Numerical Analysis, 2002
- Balanced Implicit Methods for Stiff Stochastic SystemsSIAM Journal on Numerical Analysis, 1998
- Numerical Integration of Stochastic Differential EquationsPublished by Springer Science and Business Media LLC ,1995
- Numerical integration of Hamiltonian systems with external noisePhysics Letters A, 1994
- Numerical Hamiltonian ProblemsPublished by Springer Science and Business Media LLC ,1994
- Numerical Solution of Stochastic Differential EquationsPublished by Springer Science and Business Media LLC ,1992
- Symplectic integrators for Hamiltonian problems: an overviewActa Numerica, 1992
- Symplectic integration of Hamiltonian systemsNonlinearity, 1990
- Mathematical Methods of Classical MechanicsPublished by Springer Science and Business Media LLC ,1989
- Mécanique AléatoirePublished by Springer Science and Business Media LLC ,1981