A unified view of hierarchy approach and formula of differentiation

Yan, Yun-An; Wang, Haobin; Shao, Jiushu

doi:10.1063/1.5126341

Title: A unified view of hierarchy approach and formula of differentiation

Journal Article · 24 October 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5126341 · OSTI ID:1571839

;

; Shao, Jiushu

The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1571839

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 151; ISSN 0021-9606

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

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