Numerical scheme with high order accuracy for solving a modified fractional diffusion equation

In recent years, some researchers have developed various numerical schemes to solve the modified fractional diffusion equation. For the numerical solutions of the modified fractional diffusion equation, there are already some important progresses. In this paper, a numerical scheme with second order temporal accuracy and fourth order spatial accuracy is developed to solve a modified fractional diffusion equation; the convergence, stability and solvability of the numerical scheme are analyzed by Fourier analysis; the theoretical results extremely consistent with the numerical experiment.