Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements (Contemporary Mathematics, 2024)
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.
Keywords: B-Splines, space fractional diffusion equation, orthogonal collocation, finite elements