Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements

In this paper, we consider the solution of the space fractional diffusion equation using orthogonal collocation on finite elements (OCFE) with quadratic B-spline basis functions. The main advantage of quadratic B-splines is that they have good interpolating properties and can be easily adapted for solving problems on non-uniform grids. The method is unconditionally stable and its convergence is also discussed. It is of order (3 − α) for 1 < α < 2. We present various linear and nonlinear examples. The solutions compared favourably with previous results in the literature.