A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations

Abstract

A cubic trigonometric B-spline collocation approach for the numerical solution of fractional sub-diffusion equation is presented in this paper. The approach is based on the usual finite difference scheme to discretize the time derivative while the approximation of the second-order derivative with respect to space is obtained by the cubic trigonometric B-spline functions with the help of Grünwald–Letnikov discretization of the Riemann–Liouville derivative. The scheme is shown to be stable using the Fourier method and the accuracy of the scheme is tested by application to a test problem. The results of the numerical test verify the accuracy and efficiency of the proposed algorithm.