A class of second order difference approximations for solving space fractional diffusion equations

Tian, WenYi; Zhou, Han; Deng, Weihua

doi:10.1090/S0025-5718-2015-02917-2

A class of second order difference approximations for solving space fractional diffusion equations
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by WenYi Tian, Han Zhou and Weihua Deng PDF

Math. Comp. 84 (2015), 1703-1727 Request permission

Abstract:

A class of second order approximations, called the weighted and shifted Grünwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established. Several numerical examples are implemented to test the efficiency of the numerical schemes and confirm the convergence order, and the numerical results for variable coefficients problem are also presented.

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