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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