Du Fort-Frankel Scheme for the Variable Order Time Fractional Diffusion Equation

In this paper, the variable order time-fractional diffusion equations in a finite domain are considered. A Du Fort-Frankel finite difference method is introduced to solve these equations. The stability condition for this scheme is discussed and proved via the approach of Fourier analysis. Numerical examples are prepared to illsutrate that the numerical method is computationally efficient.