椭圆方程初值问题的一个数值解法  

A Numerical Method for Initial Value Problem of Elliptic Equation

作　　者：张晔[1] 马富明[1] 

机构地区：[1]吉林大学数学研究所

出　　处：《吉林大学学报（理学版）》2008年第5期809-815,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10431030)

摘　　要：讨论一类椭圆型方程初值问题的数值求解.由于这类问题的严重不适定性,其求解过程中必须采取适当的正则化.利用算子谱分解的特定形式,对问题的解进行分解,在一个特定子空间上提出一种正则化方法,并对Laplace方程初值问题进行数值计算.数值结果表明该方法可行、有效.We considered an initial value problem of elliptic equation. This problem is severely ill-posed, so we must use regularization in the solving process. When the spectrum of the operator consided here satisfied some proper conditions, we made use of a specific form of spectrum decomposition to decompose the solution, and introduced a regularization method in a specifical subspace. We used this method to develop a numerical computation for an initial value problem of Laplace equation. The numerical experiments demonstrate that this method is efficient.

关 键 词：椭圆方程 不适定问题 正则化方法 微分方程数值解 

分 类 号：O241.3[理学—计算数学]