Based on backward difference and Crank-Nicolson scheme

a three-level fifteen-point implicit difference scheme for two- dimensional diffusion equation is proposed. The truncation error is obtained by Taylor expansion

and the compatibility of the scheme is proved

then the unconditional stability of the scheme is proved by Fourier transform and Von Neumann condition. Since the three-level difference scheme needs two-level starting conditions

two-dimensional Saul ′ ev difference scheme is used as the starting scheme of three-level fifteen-point implicit difference scheme in numerical experiments. Numerical experiments show that the combination of Saul ′ ev scheme and three-level fifteen-point difference scheme has small error and high accuracy

and the change of network ratio has little effect on the error.