AM  Vol.4 No.11 , November 2013
Pseudo-Spectral Method for Space Fractional Diffusion Equation
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.


Cite this paper
Huang, Y. and Zheng, M. (2013) Pseudo-Spectral Method for Space Fractional Diffusion Equation. Applied Mathematics, 4, 1495-1502. doi: 10.4236/am.2013.411202.
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