Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations

Authors:
Han Zhou;Wenyi Tian;Weihua Deng
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China 730000;School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China 730000;School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China 730000
Venue:
Journal of Scientific Computing
Year:
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.