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Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation

Published online by Cambridge University Press:  06 March 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
Zhi-Zhong Sun*
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China
*
*Corresponding author. Email addresses: renjincheng2001@126.com (J. Ren), zzsun@seu.edu.cn (Z. Z. Sun)
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Abstract

Some efficient numerical schemes are proposed to solve one-dimensional and two-dimensional multi-term time fractional diffusion-wave equation, by combining the compact difference approach for the spatial discretisation and an L1 approximation for the multi-term time Caputo fractional derivatives. The unconditional stability and global convergence of these schemes are proved rigorously, and several applications testify to their efficiency and confirm the orders of convergence.

Keywords

65M0665M1265M15Multi-term time fractional diffusion-wave equationcompact difference schemediscrete energy methodconvergence
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 1 , February 2015 , pp. 1 - 28
Copyright
Copyright © Global-Science Press 2015 

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