Numerical simulation with the second order compact approximation of first order derivative for the modified fractional diffusion equation

In this paper, based on the second order compact approximation formula of first order derivative, the numerical simulation method with second order temporal accuracy and fourth order spatial accuracy is developed to simulate the modified fractional diffusion equation; the convergence, stability and solvability of the numerical simulation method are analyzed by Fourier analysis and algebraic theory, respectively; the theoretical results extremely consistent with the numerical experiment.