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Two-level difference scheme for the two-dimensional Fokker–Planck equation

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  • Butt, Muhammad Munir

Abstract

In this paper, we propose a two-level difference scheme for solving the two-dimensional Fokker–Planck equation. This equation is a parabolic type equation which governs the time evolution of probability density function of the stochastic processes. In addition, these equations preserve positivity and conservation. The Chang–Cooper discretization scheme is used, which ensures second-order accuracy, positiveness, and satisfies the conservation of the total probability. In particular, we investigate a two-level scheme with factor-three coarsening strategy. With coarsening by a factor-of-three we obtained simplified inter-grid transfer operators and thus have a significant reduction in CPU time. Numerical experiments are performed to validate efficiency of the proposed Chang–Cooper two-level algorithms to stationary and time-dependent Fokker–Planck equations, respectively.

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  • Butt, Muhammad Munir, 2021. "Two-level difference scheme for the two-dimensional Fokker–Planck equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 276-288.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:276-288
    DOI: 10.1016/j.matcom.2020.09.001
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    References listed on IDEAS

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    1. Souvik Roy & Mario Annunziato & Alfio Borzì & Christian Klingenberg, 2018. "A Fokker–Planck approach to control collective motion," Computational Optimization and Applications, Springer, vol. 69(2), pages 423-459, March.
    2. Sepehrian, Behnam & Radpoor, Marzieh Karimi, 2015. "Numerical solution of non-linear Fokker–Planck equation using finite differences method and the cubic spline functions," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 187-190.
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