非线性常微分方程边值问题的最优化算法  

Optimization Algorithm of Boundary Value Problem for Nonlinear Ordinary Differential Equations

作　　者：侯祥林[1] 钱颖[1] 吴海涛[1] 

机构地区：[1]沈阳建筑大学理学院,沈阳110168

出　　处：《工程数学学报》2010年第4期663-668,共6页Chinese Journal of Engineering Mathematics

基　　金：辽宁省自然科学基金(20072011);国家"十一五"科技支撑计划重点项目(2008BAJ09B02-2);辽宁省教育厅项目(L2010445)~~

摘　　要：本文提出了一种新的优化方法以精确地解决微分方程的边值问题。针对非线性微分方程边值问题打靶法的不足,以未知的部分初始条件为设计变量,以给定的边界函数值与设计变量之间的关系,形成复杂嵌套式程式化的目标函数,建立了求解未知初始条件的优化问题,并采用Visual Basic6.0语言编制了求解未知初始条件的程序,给出了典型算例,并通过比较,验证了本文求解方法的正确性。In this paper, an optimization method is applied to accurately solve a boundary value problem of ordinary differential equations. In view of the weakness of the shooting method, this study treats the initial conditions of the unknown parts as design variables and conducts complicated objective function based on the relationship between the given boundary values and design variables. And therefore, a new optimization algorithm to compute initial conditions of unknown parts is proposed, which is finally verified by employing Visual Basic6.0 to design a universe program, providing typical examples and making comparison with the existent results.

关 键 词：非线性微分方程 边值问题 优化方法 程序设计 

分 类 号：O175.8[理学—数学] O224[理学—基础数学]