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Numerical solution of non-linear Fokker–Planck equation using finite differences method and the cubic spline functions

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  • Sepehrian, Behnam
  • Radpoor, Marzieh Karimi

Abstract

In this paper we proposed a finite difference scheme for solving the nonlinear Fokker–Planck equation. We apply a finite difference approximation for discretizing spatial derivatives. Then we use the cubic C1-spline collocation method which is an A-stable method for the time integration of the resulting nonlinear system of ordinary differential equations. The proposed method has second-order accuracy in space and fourth-order accuracy in time variables. The numerical results confirm the validity of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:187-190
    DOI: 10.1016/j.amc.2015.03.062
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    Cited by:

    1. Ureña, Francisco & Gavete, Luis & Gómez, Ángel García & Benito, Juan José & Vargas, Antonio Manuel, 2020. "Non-linear Fokker-Planck equation solved with generalized finite differences in 2D and 3D," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    2. 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.
    3. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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