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

[摘要] 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. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-10

[关键词] fractional diffusion equation;sub-diffusion;implicit difference approximation;Fourier method;stability;convergence