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Journal of Scientific Computing

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01-07-2013

Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations

Authors: Han Zhou, WenYi Tian, Weihua Deng

Published in: Journal of Scientific Computing | Issue 1/2013

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Abstract

In this paper, a compact difference operator, termed CWSGD, is designed to establish the quasi-compact finite difference schemes for approximating the space fractional diffusion equations in one and two dimensions. The method improves the spatial accuracy order of the weighted and shifted Grünwald difference (WSGD) scheme (Tian et al., arXiv:1201.5949) from 2 to 3. The numerical stability and convergence with respect to the discrete L ² norm are theoretically analyzed. Numerical examples illustrate the effectiveness of the quasi-compact schemes and confirm the theoretical estimations.

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Title: Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations
Authors: Han Zhou
WenYi Tian
Weihua Deng
Publication date: 01-07-2013
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2013
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9661-0

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