An Extended Cubic B-spline Collocation Scheme for Time Fractional Sub-diffusion Equation

摘要

In this paper, an extended cubic B-spline scheme is developed to solve the time fractional sub-diffusion equation. The time fractional derivative is represented using Caputo's formula and the discretization utilizes the θ-weighted scheme. The scheme is unconditionally stable and the convergence is shown to be of second order. The results of numerical experiments indicate the effectiveness of the proposed method.