高维热传导方程的高精度交替方向隐式方法  

A high-order alternating direction implicit method for solving the high dimensional heat equations

作　　者：葛永斌[1] 田振夫[1] 吴文权[2] 

机构地区：[1]宁夏大学数学计算机学院,银川750021 [2]上海理工大学动力工程学院,上海200093

出　　处：《上海理工大学学报》2007年第1期55-58,共4页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(10502026;10662006;50576055)

摘　　要：提出了数值求解二维和三维热传导方程的高精度交替方向隐式(ADI)方法,其空间为四阶精度、时间为二阶精度,并通过Neumann方法证明是无条件稳定的.该方法沿每个空间方向只涉及3个网格基架点,因此可以重复采用TDMA算法,大大节省了计算时间.数值实验验证了该方法的高阶精度,并与二阶的Peaceman-Rachford格式、Douglas格式及Crank-Nicolson格式进行了比较.A high-order alternating direction implicit （ADI） method for solving two or three dimensional heat equations is proposed. The method is fourth order in space and second order in time. Avon Neumann analysis shows that the method is unconditionally stable. It permits to use TDMA algorithm with a considerable save of computing time. Numerical experiments are conducted to test its high accuracy and to compare it with the second order Peaceman-Rachford scheme, Doulgas scheme and Crank -Nicolson scheme.

关 键 词：热传导方程 高阶紧致格式 交替方向隐式方法 稳定性 

分 类 号：O241.82[理学—计算数学]