p维抛物型方程改进的Douglas格式  

Improved Douglas Implicit Difference Method for Solving Parabolic Equation of p-Dimension

作　　者：陈贞忠[1] 

机构地区：[1]新乡学院数学系,河南新乡453000

出　　处：《河南大学学报（自然科学版）》2011年第5期451-456,共6页Journal of Henan University:Natural Science

基　　金：河南省教育厅自然科学基金资助项目(2008B110016)

摘　　要：研究了一个对任何p维空间变量的抛物型方程都适用的改进的Douglas格式.首先综合运用算子方法,给出了改进的Douglas差分格式算法,接着利用Fourier稳定性分析方法讨论了差分格式的稳定性和收敛性,且收敛阶为O(τ2+h4),最后给出了数值例子,数值结果和理论结果是吻合的.The paper is devoted to an improved Douglas method which is applied to a parabolic equation with any p-dimensional space variables.Firstly,the improved Douglas difference scheme algorithm is given by the combination of operator methods.Secondly,the stability and convergence of ADI difference scheme are achieved by using Fourier method,and the convergence order is O（τ2＋h4）.Finally,a numerical example demonstrates the theoretical results.

关 键 词：交替方向隐式差分格式 截断误差 绝对稳定 

分 类 号：O241.82[理学—计算数学]