高维抛物型方程的一个高精度恒稳定的交替方向格式  

An ADI Scheme with High Accuracy and Absolute Stability for Solving High Dimensional Parabolic Equations

作　　者：张星 单双荣[2] 

机构地区：[1]福建生物工程职业技术学院基础部,福州350002 [2]华侨大学数学科学学院,福建泉州362021

出　　处：《工程数学学报》2011年第1期61-66,共6页Chinese Journal of Engineering Mathematics

基　　金：国务院侨务办公室科研基金资助(04QZR09)~~

摘　　要：本文对高维抛物型方程构造了一个高精度恒稳定的交替方向格式.当2≤p≤4时,格式的局部截断误差阶可达到O(τ2+h4),当p=3时,将Richardson外推法应用于本文格式,得到了O(τ3+h6)阶精度的近似解.最后通过数值实例验证了我们对所得格式所作的理论分析是正确的.In this paper,an ADI scheme with high accuracy and absolute stability is constructed for solving high dimensional parabolic equations.As p varies from 2 to 4,the scheme is absolutely stable and the truncation error can reach the order of O（τ2 ＋ h4） at the maximum.When p is 3,the Richardson＇s extrapolation method is successfully applied to the scheme and the approximate solution with accuracy O（τ3＋h6） is attained through an extrapolation.The correctness of the proposed scheme is verified by numerical examples.

关 键 词：高维抛物型方程 交替方向格式 高精度 恒稳定 

分 类 号：O241.8[理学—计算数学]