常系数扩散方程三层十五点差分格式的稳定性  

Stability of Three-level Fifteen-point Difference Scheme for Diffusion Equations with Constant Coefficients

作　　者：刘莹 毕卉 LIU Ying;BI Hui(School of Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2023年第5期143-149,共7页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然科学基金联合引导项目(LH2020A015)。

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。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.

关 键 词：三层十五点差分格式 二维扩散方程 稳定性 误差估计 Saul′ev格式 

分 类 号：O241.3[理学—计算数学]