摘要
微分方程的边值问题在一定条件下可转化为泛函极值问题 ,将此泛函极值问题转化为 Hamilton形式 ,应用互补变分原理 ,给出具有物理意义的量的上界和下界估计。只要适当地选取试验函数 ,就可以较精确地估计出物理量的上界和下界。以一类 Schr dinger型问题为例 ,应用互补变分原理进行理论比较和数值试验。结果表明 。
The boundary value problem of differential equation can be transformed into that of the functional extreme value under certain conditions. After transforming it into Hamilton differential system, the upper bound and the lower bound of the value under certain physical backgrounds can be estimated by applying the complementary variational principles. As long as the testing functions are chosen, the upper bound and lower bound can be estimated accurately. To take one kind of Schrodinger problem as an example, the upper bound and lower bound can be compared in theory and tested in numerical value. The result shows that the estimation is satisfactory.
出处
《解放军理工大学学报（自然科学版）》
EI
2004年第3期93-97,共5页
Journal of PLA University of Science and Technology(Natural Science Edition)
关键词
泛函极值问题
凸-凹鞍型泛函
互补变分原理
试验函数
functional extreme value problem
convex-concave saddle function
complementary variational principles
testing function
