An  Effcient Second‑Order Convergent Scheme for One‑Side Space Fractional Difusion Equations with Variable Coefcient

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	An Effcient Second‑Order Convergent Scheme for One‑Side Space Fractional Difusion Equations with Variable Coefcient
	Lin, X.-L.; Lyu, P.; Ng, M. K.; Sun, H. W.; Vong, S. W.
	2020-06-01
Source Publication	Communications on Applied Mathematics and Computation
ISSN	2096-6385
Pages	215-239
Abstract	In this paper, a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients. In the presented scheme, the Crank–Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald–Letnikov spatial discretization are employed. Theoretically, the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients. Moreover, a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme. The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes, so that the Krylov subspace solver for the preconditioned linear systems converges linearly. Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.
Keyword	One-side space fractional difusion equation Variable difusion coefcients
URL	View the original
Language	英語English
The Source to Article	PB_Publication
PUB ID	50008
Document Type	Journal article
Collection	University of Macau
Corresponding Author	Lyu, P.
Recommended Citation GB/T 7714	Lin, X.-L.,Lyu, P.,Ng, M. K.,et al. An Effcient Second‑Order Convergent Scheme for One‑Side Space Fractional Difusion Equations with Variable Coefcient[J]. Communications on Applied Mathematics and Computation, 2020, 215-239.
APA	Lin, X.-L.., Lyu, P.., Ng, M. K.., Sun, H. W.., & Vong, S. W. (2020). An Effcient Second‑Order Convergent Scheme for One‑Side Space Fractional Difusion Equations with Variable Coefcient. Communications on Applied Mathematics and Computation, 215-239.
MLA	Lin, X.-L.,et al."An Effcient Second‑Order Convergent Scheme for One‑Side Space Fractional Difusion Equations with Variable Coefcient".Communications on Applied Mathematics and Computation (2020):215-239.

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