A Lie algebraic approach for a class of highly oscillatory stochastic Hamiltonian systems

doi:10.7523/j.issn.2095-6134.2019.01.002

›› 2019, Vol. 36 ›› Issue (1): 5-10.DOI: 10.7523/j.issn.2095-6134.2019.01.002

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A Lie algebraic approach for a class of highly oscillatory stochastic Hamiltonian systems

RUAN Jialin, WANG Lijin

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2017-09-26 Revised:2018-01-04 Online:2019-01-15
Supported by:
Supported by the National Nature Science Foundation of China (11471310,11071251)

Abstract

Abstract: In this work, we propose a Lie algebraic approach for numerically solving a class of highly oscillatory stochastic Hamiltonian systems (SHSs). For a concrete highly oscillatory SHS, we construct two numerical schemes based on the Lie algebraic approach, and prove their near preservation of the symplecticity. We also show by numerical tests their root mean-square convergence orders, as well as their effectiveness and merits in solving the highly oscillatory SHS.

Key words: numerical solutions of stochastic differential equations, stochastic Hamiltonian systems, highly oscillatory SDEs, operator splitting methods, Lie algebraic approach

CLC Number:

O241.8

RUAN Jialin, WANG Lijin. A Lie algebraic approach for a class of highly oscillatory stochastic Hamiltonian systems[J]. , 2019, 36(1): 5-10.

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A Lie algebraic approach for a class of highly oscillatory stochastic Hamiltonian systems

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