二阶线性常微分方程的两点边值问题的新解法  

A New Method for Solving Two-point Boundary Value Problems of Second-order Linear Ordinary Differential Equation

作　　者：马翠[1] 周先东[2] 宋丽娟[1] 

机构地区：[1]第三军医大学数学与生物数学教研室,重庆400038 [2]云南省军区德宏军分区77332部队,云南德宏678400

出　　处：《西南师范大学学报（自然科学版）》2010年第4期74-78,共5页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：基于变分原理,将二阶线性常微分方程的两点边值问题转化为等价的变分问题（即泛函极值问题）,利用两点三次Hermite插值构造一个逼近可行函数的近似函数,从而将问题转化为一个多元单目标优化问题,最后运用粒子群优化算法求解该优化问题,由此求得二阶线性常微分方程的两点边值问题的近似解.数值实验表明该方法优于传统的里兹法和有限差分方法.This context proposed a variational problem which was equal to the question of second-order linear ordinary differential equations based on variational principle.And found an approximate function by two-point cubic Hermit interpolation.Afterwards,the second-order linear ordinary differential equations problem was transformed to a multivariate single object optimization problem,which can be solved by particle swarm optimization.The solution was the approximate solution of second-order linear ordinary differ-ential equations.It is very satisfied by comparing it with Ritz method and finite difference method.This method was different from finite difference method and finite element method,it applies intelligent optimization algorithm to solving differential equations,and the domain of intelligent optimization algorithm was extended.

关 键 词：二阶线性常微分方程 两点边值问题 粒子群优化算法 变分问题 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]