作者:刘莹，毕卉
Authors:LIUYing,BIHui摘要:基于向后差分格式和 Crank-Nicolson 格式对二 维扩散方程提出 一 种三层十五点隐式差分格式 。采用 泰勒展开求出截断误差 ,证明了该格式的相容性 ,接着用傅里叶变换和 Von Neumann 条件证明了该格式的无条件 稳定性 。 由于三层差分格式需要两层启动条件 ,在数值实验中 ,利用二 维 Saul ′ev 差分格式作为三层十五点隐式差 分格式的启动格式 。数值试验表明 Saul ′ev 格式与三层十五点差分格式相结合误差小 ,精度高 , 并且网比的变化对 误差的影响不大。
Abstract: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.

PDF全文下载地址:

可免费Download/下载PDF全文