关于修正局部Crank-Nicolson法对于二维热传导方程的应用的注记

A Remark on a Corrected Local C-N Method for the Two-dimensional Heat Equation

在《修正局部Crank-Nicolson法对于二维热传导方程的应用》一文中,作者把一维和二维热传导方程半离散化后,借助于泛函分析中Lie乘积公式,利用矩阵分裂得到修正局部Crank-Nicolson格式,该格式是显示差分格式,不需要直接解以大型矩阵为系数矩阵的线性方程组,从而计算简单,计算量小,在实际问题中有较大应用价值.本文作者在学习和应用该算法时,发现关于该算法的某些结论需要修正.

This paper discussed the method and the proof of the theorems in corrected local C-N method for the two dimensional heat equation,the method is based on the Lie product by the splitting of the coefficient matrix.The method is explicit and easy,the amount of computation is small,the method has not to solve the big linear systems of the equation.This paper proposed stability and convergence of the corrected local C-N method should be corrected.