[3, 3] Padé approximation method for solving space fractional Fokker-Planck equations

Abstract The fractional Fokker–Planck equation has been used in various areas of engineering and physics. In this paper, we proposed a novel numerical scheme for solving the space fractional Fokker–Planck equation with the help of the [3, 3] Pade approximation. It is proved that the numerical method is unconditionally stable in view of the matrix analysis method. Finally, a numerical example is proposed to prove the effectiveness of the numerical scheme.

[1]  Mary F. Wheeler,et al.  Modelling and Simulation in Fluid Dynamics in Porous Media , 2013 .

[2]  Luis Vázquez Martínez,et al.  Numerical solution of two dimensional Fokker - Planck equations , 1999, Appl. Math. Comput..

[3]  Weihua Deng,et al.  Finite Element Method for the Space and Time Fractional Fokker-Planck Equation , 2008, SIAM J. Numer. Anal..

[4]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[5]  Diana Adler.  Padé approximants for operators, theory and applications , 1986 .

[6]  Rami Ahmad El-Nabulsi,et al.  The fractional Boltzmann transport equation , 2011, Comput. Math. Appl..

[7]  Richard S. Varga,et al.  Matrix Iterative Analysis , 2000, The Mathematical Gazette.

[8]  D. Kinderlehrer,et al.  THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .

[9]  E. Barkai,et al.  Fractional Fokker-Planck equation, solution, and application. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  D. Benson,et al.  Application of a fractional advection‐dispersion equation , 2000 .

[11]  Ralf Metzler,et al.  The fractional Fokker-Planck equation: dispersive transport in an external force field , 2000 .

[12]  Fawang Liu,et al.  Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term , 2010 .

[13]  R A El Nabulsi,et al.  A FRACTIONAL ACTION-LIKE VARIATIONAL APPROACH OF SOME CLASSICAL, QUANTUM AND GEOMETRICAL DYNAMICS , 2005 .

[14]  Fawang Liu,et al.  Numerical solution of the space fractional Fokker-Planck equation , 2004 .

[15]  I. Podlubny.  Fractional differential equations , 1998 .

[16]  Fawang Liu,et al.  Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations , 2009 .

[17]  Aidarkhan Kaltayev,et al.  Application of He’s Homotopy Perturbation Method for Solving Fractional Fokker-Planck Equations , 2009 .

[18]  Fawang Liu,et al.  Numerical treatment for the fractional Fokker-Planck equation , 2007 .

[19]  Fawang Liu,et al.  Finite difference approximations for the fractional Fokker–Planck equation , 2009 .