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An Efficient Second‑Order Convergent Scheme for One‑Side Space Fractional Diffusion Equations with Variable Coefficients
Lin Xuelei1; Lyu Pin2; Michael K. Ng1; Sun HW(孫海衛)3; Seak Weng Vong3
2020-06
Source PublicationCommunications on Applied Mathematics and Computation
ISSN2096-6385
Volume2Issue:2Pages: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.

KeywordOne-side Space Fractional Diffusion Equation Variable Diffusion Coefficients Stability And Convergence High-order Finite-difference Scheme Preconditioner
Subject Area数学 ; 计算数学 ; 偏微分方程数值解
Indexed BySCIE
Language英語English
Funding ProjectExponential-like Runge-Kutta methods for non-linear fractional order partial differential equations
Fulltext Access
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorSun HW(孫海衛)
Affiliation1.Hong Kong Baptist University
2.Southwestern University of Finance and Economics
3.University of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lin Xuelei,Lyu Pin,Michael K. Ng,et al. An Efficient Second‑Order Convergent Scheme for One‑Side Space Fractional Diffusion Equations with Variable Coefficients[J]. Communications on Applied Mathematics and Computation,2020,2(2):215--239.
APA Lin Xuelei,Lyu Pin,Michael K. Ng,Sun HW,&Seak Weng Vong.(2020).An Efficient Second‑Order Convergent Scheme for One‑Side Space Fractional Diffusion Equations with Variable Coefficients.Communications on Applied Mathematics and Computation,2(2),215--239.
MLA Lin Xuelei,et al."An Efficient Second‑Order Convergent Scheme for One‑Side Space Fractional Diffusion Equations with Variable Coefficients".Communications on Applied Mathematics and Computation 2.2(2020):215--239.
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