International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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A Generalized Finite Difference Method for Solving Fokker-Planck-Kolmogorov Equations

  • Zhao, Li (Department of Civil Engineering, The University of Akron) ;
  • Yun, Gun Jin (Department of Mechanical and Aerospace Engineering, Seoul National University)
  • Received : 2017.05.17
  • Accepted : 2017.07.31
  • Published : 2017.12.30
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Abstract

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

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Acknowledgement

Supported by : Seoul National University, University of Akron

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