Abstract
We present high-order symplectic schemes for stochastic Hamiltonian systems preserving Hamiltonian functions. The approach is based on the generating function method, and we show that for the stochastic Hamiltonian systems, the coefficients of the generating function are invariant under permutations. As a consequence, the high-order symplectic schemes have a simpler form than the explicit Taylor expansion schemes with the same order. Moreover, we demonstrate numerically that the symplectic schemes are effective for long time simulations.
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Anton, C., Wong, Y.S., Deng, J. (2013). Symplectic Numerical Schemes for Stochastic Systems Preserving Hamiltonian Functions. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_16
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DOI: https://doi.org/10.1007/978-3-642-41515-9_16
Publisher Name: Springer, Berlin, Heidelberg
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