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Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  20 July 2016

Gongsheng Li ,
Chunlong Sun ,
Xianzheng Jia  and
Dianhu Du
Gongsheng Li*
Affiliation:
School of Sciences, Shandong University of Technology, Zibo, Shandong 255049, China
Chunlong Sun*
Affiliation:
School of Sciences, Shandong University of Technology, Zibo, Shandong 255049, China
Xianzheng Jia*
Affiliation:
School of Sciences, Shandong University of Technology, Zibo, Shandong 255049, China
Dianhu Du*
Affiliation:
School of Sciences, Shandong University of Technology, Zibo, Shandong 255049, China
*
*Corresponding author. Email addresses:ligs@sdut.edu.cn (Gongsheng Li), sunchunlong527@163.com (Chunlong Sun), kathy1978@126.com (Xianzheng Jia), dudianhu@126.com (Dianhu Du)
*Corresponding author. Email addresses:ligs@sdut.edu.cn (Gongsheng Li), sunchunlong527@163.com (Chunlong Sun), kathy1978@126.com (Xianzheng Jia), dudianhu@126.com (Dianhu Du)
*Corresponding author. Email addresses:ligs@sdut.edu.cn (Gongsheng Li), sunchunlong527@163.com (Chunlong Sun), kathy1978@126.com (Xianzheng Jia), dudianhu@126.com (Dianhu Du)
*Corresponding author. Email addresses:ligs@sdut.edu.cn (Gongsheng Li), sunchunlong527@163.com (Chunlong Sun), kathy1978@126.com (Xianzheng Jia), dudianhu@126.com (Dianhu Du)

Abstract

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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.

Keywords

Multi-term time fractional diffusionfinite difference schemespectral radiusstability and convergencenumerical simulation

MSC classification

Secondary: 35R11: Fractional partial differential equations 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 3 , August 2016 , pp. 337 - 357
Copyright
Copyright © Global-Science Press 2016 

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