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.

Huang, Y. and Zheng, M. (2013) Pseudo-Spectral Method for Space Fractional Diffusion Equation.

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