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A Semi-Lagrangian Method for 3-D Fokker Planck Equations for Stochastic Dynamical Systems on the Sphere

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Abstract

In this paper, we consider stochastic dynamical systems on the sphere and the associated Fokker–Planck equations. A semi-Lagrangian method combined with a Finite Volume discretization of the sphere is presented to solve the Fokker–Planck equation. The method is applied to a typical problem in fiber dynamics and textile production. The numerical results are compared to explicit solutions and Monte-Carlo solutions.

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Acknowledgments

This work has been supported by Deutsche Forschungsgemeinschaft (DFG), KL 1105/18-1 and by Bundesministerium für Bildung und Forschung (BMBF), Verbundprojekt OPAL.

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Authors and Affiliations

  1. Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 , Kaiserslautern, Germany

    A. Roth, A. Klar, B. Simeon & E. Zharovsky

  2. Fraunhofer ITWM, Fraunhoferplatz 1, 67663 , Kaiserslautern, Germany

    A. Klar

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  1. A. Roth
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  2. A. Klar
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  3. B. Simeon
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  4. E. Zharovsky
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Correspondence to A. Roth.

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Roth, A., Klar, A., Simeon, B. et al. A Semi-Lagrangian Method for 3-D Fokker Planck Equations for Stochastic Dynamical Systems on the Sphere. J Sci Comput 61, 513–532 (2014). https://doi.org/10.1007/s10915-014-9835-z

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  • DOI: https://doi.org/10.1007/s10915-014-9835-z

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