TITLE:
Pseudo-Spectral Method for Space Fractional Diffusion Equation
AUTHORS:
Yiting Huang, Minling Zheng
KEYWORDS:
Riemann-Liouville Derivative; Pseudo-Spectral Method; Collocation Method; Fractional Diffusion Equation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11,
November
5,
2013
ABSTRACT: This paper presents a numerical scheme for space
fractional diffusion equations (SFDEs) based on pseudo-spectral method. In this
approach, using the Guass-Lobatto nodes, the unknown function is approximated
by orthogonal polynomials or interpolation polynomials. Then, by using
pseudo-spectral method, the SFDE is reduced to a system of ordinary
differential equations for time variable t.
The high order Runge-Kutta scheme can be used to solve the system. So, a high
order numerical scheme is derived. Numerical examples illustrate that the
results obtained by this method agree well with the analytical solutions.