A Semianalytic Meshless Approach to the Transient Fokker-planck Equation
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چکیده
A semianalytic partition of unity finite element method (PUFEM) is presented to solve the transient FokkerPlanck equation (FPE) for high-dimensional nonlinear dynamical systems. Meshless spatial discretization of the PUFEM is employed to develop linear ordinary differential equations for the time varying coefficients of the local shape functions. A similarity transformation to the modal coordinates is shown to reveal numerous spurious modes in the eigenspace of the discretized FPE operator. The identification and elimination of these modes leads to an analytical solution of the ODEs obtained from the spatial discretization in terms of the remaining admissible modes, and a significant order-reduction in the transient problem. The initial equationerror resulting from the set of admissible modes is shown to be an upper bound for all time, and thus the reduced set is sufficient for the approximation for all time.
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تاریخ انتشار 2007