二维热传导方程的紧ADI法  

Compact ADI Method for Solving Heat Equation with Two Dimensions

作　　者：王洁[1] 

机构地区：[1]台州学院数学与信息工程学院,浙江临海317000

出　　处：《台州学院学报》2014年第3期12-15,共4页Journal of Taizhou University

基　　金：台州学院青年项目(2013QN09)

摘　　要：对二维热传导方程进行紧交替方向有限差分,该方法在空间方向上具有四阶精度,在时间方向上具有二阶精度.证明了当rx,ry≥1/6时该有限差分解收敛于连续解.数值例子验证了该有限差分法具有高阶精度.A high order algorithin is discussed in the paper. This algorithm has the accuracy of four-order in space and two-order in time. The finite difference scheme can be solved by ADI method. The convergence of finite difference solution to the continuous solution is proved when it is between 1/6 and 5/6. A numerical example is shown the high accuracy of the finite difference in the last section.

关 键 词：二维热传导方程 紧ADI法 高阶精度 收敛性 

分 类 号：O241.82[理学—计算数学]