Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique

Abstract

The purpose of this work is to find the numerical solution of the Caputo time-fractional diffusion equation using the modified cubic exponential B-spline (CExpB-spline) collocation technique. First, the CExpB-spline functions are modified and then used to discretize the space derivatives. Three numerical examples are considered for checking the efficiency and accuracy of the method. The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. Von Neumann stability is carried out which gives the guarantee that the technique is unconditionally stable. The rate of convergence is also obtained. Furthermore, this technique is efficient and requires less storage.

Keywords

• caputo time-fractional diffusion equation
• collocation technique
• cexpb-spline functions
• stability analysis