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A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations

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      Abstract

      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.

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      Journal
      2012-01-28
      2012-03-07
      1201.5949

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      26A33, 65L12, 65L20
      24 Pages
      math.NA

      Numerical & Computational mathematics

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