Numerical methods for the two-dimensional multi-term time-fractional diffusion equations

In this paper, we consider a numerical approach based on the matrix transfer method for numerical solution of multi-term time-fractional diffusion equations (MT-TFDEs). The semi- and fully-discrete schemes are developed by using the classical finite difference method and the matrix transfer technique. The unconditional stability and convergence of these two schemes are discussed and theoretically proved. The technique is then extended to MT-TFDEs with fractional Laplace operator. Numerical examples are given to validate and investigate the efficiency and the accuracy of the developed schemes. The results indicate that the present schemes are very effective for modeling and simulation of the MT-TFDEs with integral or fractional Laplacians.