二维热传导方程隐式差分格式系数矩阵特征值的求取  

Matrix eigenvalues of implicit difference scheme for two-dimensional heat conduction equation

作　　者：冯凤萍[1] 周瑞芬[2] 

机构地区：[1]大庆石油学院数学系,黑龙江大庆163318 [2]大庆石油学院机械科学与工程学院,黑龙江大庆163318

出　　处：《大庆石油学院学报》2005年第3期88-89,93,127,共4页Journal of Daqing Petroleum Institute

基　　金：黑龙江省自然科学基金项目(A00-19)

摘　　要：给出了二维热传导方程隐式差分格式.对该差分格式的未知量和右端项以矩阵形式表示,可得出差分格式的矩阵表示新形式.原系数矩阵的特征值和特征向量的求取变得简便,为进一步分析差分格式的稳定性和利用迭代法求该类线性方程组时的收敛速度分析奠定了基础.The implicit difference scheme for two-dimensional heat-conduction equation is presented. Denoting the unknown by a matrix and the right terms by a matrix, a new matrix form of difference scheme is acquired. A very simple method is derived to get the eigenvalues and eigenvectors of this kind of coefficient matrix. It lays a foundation for further analysis of stability of difference scheme and convergence speed analysis when we solve the system of linear equations with the application of iterative methods.

关 键 词：隐式差分格式 矩阵特征值 稳定性 二维热传导方程 

分 类 号：O177[理学—数学]