Year: 2021
Author: Rui-Lian Du, Zhi-Zhong Sun
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 647–673
Abstract
A fast temporal second-order compact alternating direction implicit (ADI) difference scheme is proposed and analysed for 2D time fractional mixed diffusion-wave equations. The time fractional operators are approximated by mixed fast $L2$-$1_σ$ and fast $L1$-type formulas derived by using the sum-of-exponentials technique. The spatial derivatives are approximated by the fourth-order compact difference operator, which can be implemented by an ADI approach with relatively low computational cost. The resulting fast algorithm is computationally efficient in long-time simulations since the computational cost is significantly reduced. Numerical experiments confirm the effectiveness of the algorithm and theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.271220.090121
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 647–673
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Time fractional mixed diffusion-wave equations SOEs technique ADI difference scheme stability convergence.