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A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
A class of second order approximations, called the weighted and shifted
Gr\"{u}nwald difference 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
testify the efficiency of the numerical schemes and confirm the convergence
order, and the numerical results for variable coefficients problem are also
presented.Comment: 24 Page
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