Stability of Three-level Fifteen-point Difference Scheme for Diffusion Equations with Constant Coefficients - LIUYing; BIHui (Journal of Harbin University of Science and Technology)
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.