For stochastic systems, the Fokker–Planck equation (FPE) is used to describe the system dynamics. The FPE is a partial differential equation, which is a function of all the variables in state space and of time. To solve the FPE, several methods are used, including finite elements, moment neglect methods, and cumulant neglect methods. This paper will study the cumulant neglect equations, which are derived from the FPE. It will be shown that the cumulant neglect method, while being a useful and popular tool for studying the system response, introduces several nonphysical artifacts.
Continuation Method on Cumulant Neglect Equations
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 30, 2017; final manuscript received October 30, 2017; published online July 26, 2018. Assoc. Editor: Hiroshi Yabuno.
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Perkins, E., and Fitzgerald, T. (July 26, 2018). "Continuation Method on Cumulant Neglect Equations." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090913. https://doi.org/10.1115/1.4038895
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