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Finite difference method for time-fractional Klein-Gordon equation on an unbounded domain using artificial boundary conditions

Yan, Yubin
; 
Peng, Ding
; 
Yan, Yuyuan
; 
Liang, Zongqi
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Jimei University; University of Chester
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2022-11-09
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Mathematics
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Abstract
A finite difference method for time-fractional Klein-Gordon equation with the fractional order $\alpha \in (1, 2]$ on an unbounded domain is studied. The artificial boundary conditions involving the generalized Caputo derivative are derived using the Laplace transform technique. Stability and error estimates of the proposed finite difference scheme are proved in detail by using the discrete energy method. Numerical examples show that the artificial boundary method is a robust and efficient method for solving the time-fractional Klein-Gordon equation on an unbounded domain.
Citation
Ding, P., Yan, Y., Liang, Z., & Yan, Y. (2023). Finite difference method for time-fractional Klein-Gordon equation on an unbounded domain using artificial boundary conditions. Mathematics and Computers in Simulation, 205, 902-925. https://doi.org/10.1016/j.matcom.2022.10.030
Publisher
Elsevier
Journal
Mathematics and Computers in Simulation
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http://hdl.handle.net/10034/627305
DOI
10.1016/j.matcom.2022.10.030
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Article
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0378-4754
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https://www.sciencedirect.com/science/article/pii/S037847542200444X?via%3Dihub