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An extension of the Gegenbauer pseudospectral method for the time fractional Fokker‐Planck equation
Author(s) -
Izadkhah Mohammad Mahdi,
SaberiNadjafi Jafar,
Toutounian Faezeh
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4656
Subject(s) - mathematics , chebyshev pseudospectral method , fokker–planck equation , chebyshev polynomials , mathematical analysis , pseudo spectral method , spectral method , matrix (chemical analysis) , boundary value problem , chebyshev equation , chebyshev filter , gauss pseudospectral method , pseudospectral optimal control , orthogonal polynomials , partial differential equation , fourier transform , classical orthogonal polynomials , composite material , fourier analysis , materials science
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.