An implicit numerical scheme for a class of multi-term time-fractional diffusion equation

Abstract

In this work, we study an implicit numerical scheme for a class of multi-term time-fractional diffusion equation, where the fractional derivatives are described in the Caputo sense. The numerical scheme is constructed based on Crank-Nicolson finite difference method in time and exponential B-spline method in space. It is proved that the proposed scheme is unconditionally stable and convergent with second-order in space and (2 - $ \gamma$ ) order in time. To illustrate the efficiency and accuracy of the present method, few numerical examples are presented and are compared with the other existing methods. Numerical results are presented to support theoretical analysis.