【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.更多还原

【Abstract】 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.更多还原