Pseudo-Spectral Method for Space Fractional Diffusion Equation

• 作者: Minling Zheng Yiting Huang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Riemann-Liouville DERIVATIVE Pseudo-Spectral METHOD COLLOCATION METHOD FRACTIONAL DIFFUSION EQUATION
• 年，卷（期）: 2013,（11）
• 页码范围: 1495-1502
• 页数: 8页
• 分类号: O1

摘要

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.