Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations

Abstract

A Crank-Nicolson scheme catering to solving initial-boundary value problems of a class of variable-coefficient tempered fractional diffusion equations is proposed. It is shown through theoretical analysis that the scheme is unconditionally stable and the convergence rate with respect to the space and time step is O(h2+ τ2) under a certain condition. Numerical experiments are provided to verify the effectiveness and accuracy of the scheme.