Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation

A discrete comparison principle is given for the multi-term time fractional diffusion equation, where the discrete scheme is based on L1 approximation of the multi-term temporal Caputo derivative and the standard finite difference approximation of the spatial derivative. Then we use the discrete comparison principle to give an error analysis of the discrete scheme by constructing a barrier function. The final numerical results verify our theoretical analysis under the realistic assumption that the solution of the time fractional diffusion equation has a weak singularity near the initial time t = 0.