Crank–Nicolson quasicompact schemes for one-sided tempered fractional diffusion equations (without using points outside the interval)

Abstract In this paper, we study the high-precision numerical schemes for one-sided tempered fractional diffusion equations. The Crank–Nicolson method is used for time discretization, and the fourth-order quasicompact technique is used for space direction. Theoretically, the derived numerical schemes can achieve second-order accuracy in time direction and fourth-order accuracy in space direction under certain constraints of time step and space step. In practice, when the numerical schemes are used to solve the one-sided tempered fractional diffusion equations, the accuracy of the time direction gradually approaches 2 as α decreases. Finally, some numerical examples are given to verify the theoretical analysis of the numerical schemes, and the comparison with other methods shows the improvement of the numerical schemes.