Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain. Issue 3 (20th July 2016)

• Record Type: Journal Article
• Authors: Li, Gongsheng; Sun, Chunlong; Jia, Xianzheng; Du, Dianhu
• Is Part Of: Numerical mathematics. Volume 9:Issue 3(2016)
• Page Start: 337
• Page End: 357
• Publication Date: 2016-07-20
• Subjects: 35R11, -- 65M06, -- 65M12; Multi-term time fractional diffusion, -- finite difference scheme, -- spectral radius, -- stability and convergence, -- numerical simulation; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2016.y13024
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo's definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and convergence are proved. The numerical results demonstrate the effectiveness of the theoretical analysis, and the method and technique can also be applied to other kinds of time/space fractional diffusion equations.