摘要
该文以 Schrodinger方程为例 ,分析变分迭代法的一些基本特点 .在该方法中引进了一广义拉氏乘子构造了一迭代格式 ,拉氏乘子可由变分理论最佳识别 .由于在识别拉氏乘子是应用了限制变分的概念 ,所以只能通过迭代才能得到收敛解 .为了加快收敛速度 ,可以在初始近似引入待定常数 ,而待定常数又可用各种方式最佳识别 .文中初步分析了该方法的收敛性 ,对于Schrodinger方程 ,其一阶近似即可得到
In the paper, the variational iteration method proposed by the presen t author is applied to Schrodinger equation. In this method, a general Lagrange multiplier i s introduced, which can be identified by the variational method. For nonlinear problems, the m ultiplier can be approximately determined due to the constrained variation, and the exact solutio n, therefore, has to be obtained by iteration. To speed up convergence, some a constant can be int roduced in the trial function, which can be identified by various ways. In this paper, by only one step, we obtain the well known Jost's solution for Schrodinger equation.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2001年第S1期577-583,共7页
Acta Mathematica Scientia
