高维抛物型方程的高精度恒稳定的交替格式  

Two absolutely stable ADI schemes of high accuracy for solving parabolic equation of high dimensions

作　　者：徐金平[1] 单双荣[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《福州大学学报（自然科学版）》2009年第3期331-335,共5页Journal of Fuzhou University(Natural Science Edition)

基　　金：国务院侨务办公室科研基金资助项目(04QZR09)

摘　　要：对高维抛物型方程问题,给出了两个高精度的交替方向格式(AD I格式).两个格式分别对2≤N≤4维和任意维数是恒稳定的,其局部截断误差阶均为O(2τ+h4).两个格式可以推广到一般常系数抛物型方程.数值例子与理论分析的结果相符合.In this paper, two alternating direction implicit （ADI） schemes of high accuracy are constructed for solving parabolic equation of high dimension. When the dimension N varies from two to four, the first Scheme is absolutely stable, and the second scheme is absolutely stable for the arbitrary dimension. The truncation errors of the two schemes can reach the order of O （T^2 ＋ h^4 ）. Applied the two schemes to constant coefficient parabolic equation, when the constant coefficient is limited, the two schemes are still absolutely stable. The practice samples are consistent with theoretical analysis.

关 键 词：抛物型方程 交替方向格式 精度 稳定 

分 类 号：O214.82[理学—概率论与数理统计]