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Journal of Scientific Computing

Erschienen in:

01.04.2014

Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation

verfasst von: Ya-nan Zhang, Zhi-zhong Sun

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2014

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Abstract

In this paper, a Crank–Nicolson-type compact ADI scheme is proposed for solving two-dimensional fractional subdiffusion equation. The unique solvability, unconditional stability and convergence of the scheme are proved rigorously. Two error estimates are presented. One is \(\mathcal{O }(\tau ^{\min \{2-\frac{\gamma }{2},\,2\gamma \}}+h_1^4+h^4_2)\) in standard \(H^1\) norm, where \(\tau \) is the temporal grid size and \(h_1,h_2\) are spatial grid sizes; the other is \(\mathcal{O }(\tau ^{2\gamma }+h_1^4+h^4_2)\) in \(H^1_{\gamma }\) norm, a generalized norm which is associated with the Riemann–Liouville fractional integral operator. Numerical results are presented to support the theoretical analysis.

Vorheriger Artikel Hydrodynamics in Porous Media: A Finite Volume Lattice Boltzmann Study

Nächster Artikel Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

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Titel: Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
verfasst von: Ya-nan Zhang
Zhi-zhong Sun
Publikationsdatum: 01.04.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9756-2

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