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Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations

Published online by Cambridge University Press:  28 May 2015

Jincheng Ren  and
Zhi-zhong Sun
Jincheng Ren*
Affiliation:
College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450000, China Department of Mathematics, Southeast University, Nanjing 210096, China
Zhi-zhong Sun*
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China
*
Corresponding author. Email address: [email protected]
Corresponding author. Email address: [email protected]

Abstract

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Some efficient numerical schemes are proposed for solving one-dimensional (1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and L1 approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

Keywords

65M0665M1265M15Multi-term time fractional sub-diffusion equationscompact /compact ADI difference schemediscrete energy methodconvergence
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 3 , August 2014 , pp. 242 - 266
Copyright
Copyright © Global-Science Press 2014

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