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|Title:||Numerical Methods for Stochastic Systems Preserving Symplectic Structure|
|Authors:||Milstein, G. N.|
Repin, Yu. M.
Tretyakov, M. V.
|Publisher:||Society for Industrial & Applied Mathematics (SIAM)|
|Citation:||Milstein G. N. Numerical Methods for Stochastic Systems Preserving Symplectic Structure / G. N. Milstein, Yu. M. Repin, M. V. Tretyakov // SIAM Journal on Numerical Analysis. — 2002. — Vol. 40. — Iss. 4. — P. 1583-1604.|
|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.|
STOCHASTIC HAMILTONIAN SYSTEMS
CONVERGENCE OF NUMERICAL METHODS
FINITE ELEMENT METHOD
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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