A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations

作者：Hafez Ramy M; Ezz Eldien Samer S; Bhrawy Ali H; Ahmed Engy A; Baleanu Dumitru^*

来源：Nonlinear Dynamics, 2015, 82(3): 1431-1440.

DOI：10.1007/s11071-015-2250-7

• Collocation method
• Jacobi polynomials
• Gauss-Lobatto quadrature
• Gauss-Radau quadrature
• Fractional Fokker-Planck equation
• Caputo fractional derivatives

In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.

• 出版日期2015-11