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.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
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)
关键词
椭圆方程
不适定问题
正则化方法
微分方程数值解
elliptic equation
ill-posed problem
regularization method
numerical solution of differentialequation
