三对角分块矩阵的性质和应用研究

On the Properties and Applications of Tridiagonal Blocked Matrix

物理性质的许多稳定过程都归结为椭圆型偏微分方程,而椭圆型方程边值问题的精确解只在一些特殊情况下可以求得,更多情况下需要近似地求解这些问题。讨论了三对角分块矩阵的相关概念及其性质,并利用差分格式给出了三对角分块矩阵在求解椭圆型方程边值问题中的应用,最后通过数值算例验证了该方法的有效性。

Many stable processes of physical properties can be attributed to elliptic partial differential equations,and the exact solutions of boundary value problems for elliptic equations can only be obtained in some special cases,requiring more approximate solutions to these problems.This article discusses the concepts and properties of tridiagonal block matrices,and uses difference schemes to provide applications of tridiagonal block matrices in solving boundary value problems of elliptic equations.Finally,the effectiveness of this method is verified through numerical examples.