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.
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