An extension of the Gegenbauer pseudospectral method for the time fractional Fokker-Planck equation

作者：Izadkhah Mohammad Mahdi^*; Saberi Nadjafi Jafar; Toutounian Faezeh

来源：Mathematical Methods in the Applied Sciences, 2018, 41(4): 1301-1315.

DOI：10.1002/mma.4656

• anomalous diffusion
• fractional Fokker-Planck equations
• Gegenbauer polynomials
• generalized Sylvester matrix equation
• global GMRES
• pseudospectral methods
• Riemman-Liouville fractional derivative

The time fractional Fokker-Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In this paper we examine pseudospectral method based on Gegenbauer polynomials and Chebyshev spectral differentiation matrix to solve numerically a class of initial-boundary value problems of the time fractional Fokker-Planck equation on a finite domain. The presented method reduces the main problem to a generalized Sylvester matrix equation, which can be solved by the global generalized minimal residual method. Some numerical experiments are considered to demonstrate the accuracy and the efficiency of the proposed computational procedure.

• 出版日期2018-3-15