修正局部Crank-Nicolson法对变系数扩散方程的应用  

Application of Modified Local Crank-Nicolson Method for Solving Variable Coefficient Diffusion Equation

作　　者：黄鹏展[1] 阿布都热西提.阿布都外力 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《吉林大学学报（理学版）》2008年第6期1068-1072,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10571148)

摘　　要：通过将所研究的偏微分方程转化为常微分方程组,利用指数函数的Trotter积公式近似该常微分方程组的系数矩阵并分离成分块小矩阵,再利用Crank-Nicolson法求得结果,推出变数扩散方程的一种新差分格式,这种格式是计算简单、无条件稳定的显格式,并讨论了此格式的若干性质.数值试验表明,所给方法计算简单、精度较高.The partial differential equation studied was first transformed into the ordinary differential equations, and then the Trotter produet formula of exponential function was used to approximate the eoeffieient matrix of these ordinary differential equations. The coefficient matrix was separated into small-block matrixes, and Crank-Nieolson method was used to obtain results. So a new difference scheme of variable eoeffieient diffusion equation was thus obtained. It is an explicit differenee seheme with simple ealeulation and uneonditional stability. Some properties of this scheme were discussed. Subsequent numerical experiment shows that the presented method possesses simple calculation and high accuracy.

关 键 词：变系数扩散方程 修正局部Crank—Nicolson法 稳定性 数值精度 

分 类 号：O241.82[理学—计算数学]