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

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.

• NN
  National Natural Science Foundation of China

  Awards: NCET-09, lzujbky-2012-k26, No. 11271173, 11271173, 10801067
• PF
  Program for New Century Excellent Talents in University

  Award: NCET-09-0438
• FR
  Fundamental Research Funds for the Central Universities

  Awards: lzujbky-2012-k26, lzujbky-2010-63, 11271173