A Fourier method for the fractional diffusion equation describing sub-diffusion

作者：Chen Chang Ming; Liu F^*; Turner I; Anh V

来源：Journal of Computational Physics, 2007, 227(2): 886-897.

DOI：10.1016/j.jcp.2007.05.012

• fractional diffusion equation
• sub-diffusion
• implicit difference approximation
• Fourier method
• stability
• convergence

In this paper, a fractional partial differential equation (FPDE) describing sub-diffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.

• 出版日期2007-12-10
• 单位厦门大学; 华南理工大学