Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients

A class of weighted finite difference methods (WFDMs) for solving a class of initial-boundary value problems of space fractional partial differential equations with variable coefficients is presented. Their stability and convergence properties are considered. It is proven that the WFDMs are unconditionally-stable for 0 ≤ r ≤ 1 2 , and conditionally-stable for 1 2 < r ≤ 1 , here r is the weighting parameter subjected to 0 ≤ r ≤ 1 . Some convergence results are given. These methods, problems and results generalize the corresponding methods, problems and results given in [7,8,10]. Some numerical examples are provided to show the effectiveness of the methods with different weighting parameters.