High-Order Local Absorbing Boundary Conditions for Fractional Evolution Equations on Unbounded Strips
Year: 2020
Author: Haixia Dong, Miao Wang, Dongsheng Yin, Qian Zhang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 664–693
Abstract
The study of this paper is two-fold. On the one hand, we reduce the subdiffusion ($0<\alpha<1$) and diffusion-wave ($1<\alpha<2$) problems on unbounded strips to initial boundary value problems (IBVPs) by deriving high-order local artificial boundary conditions (ABCs). After that, the IBVPs with our high-order local ABCs are proved to be stable in the L2-norm. On the other hand, unconditionally stable schemes are constructed to numerically solve the IBVPs by using L1 approximation to discretize the temporal derivative and using finite difference methods to discretize the spatial derivative. We provide the complete error estimates for the subdiffusion case and sketch the proof for the diffusion-wave case. To further reduce the computational and storage cost for the evaluation of the fractional derivatives, the fast algorithm presented in [14] is employed for the case of $0<\alpha<1$ and a similar algorithm for the case of $1<\alpha<2$ is first introduced in this article. Numerical examples are provided to verify the effectiveness and performance of our ABCs and numerical methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0115
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 664–693
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Subdiffusion equations diffusion-wave equations anomalous diffusion artificial boundary methods fast algorithms high-order local absorbing boundary conditions.