获得非线性微分方程显式解析解的两种新算法  

Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations

作　　者：张鸿庆[1] 闫振亚[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《应用数学和力学》2000年第12期1285-1292,共8页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展规划基金资助项目!(G19980 30 60 0 );教育部博士点基金资助项目!( 980 14119)

摘　　要：基于AC =BD的思想来求解非线性微分方程 (组 ) ·　设 Au =0为给定的待求解的方程 ,Dv=0是容易求解的方程·　如果可以获得变换u=Cv使得v满足Dv=0 ,则能够得到Au =0的解·　为了说明该种途径 ,本文举例给出几种变换CThe idea of AC=BD was applied to solve the nonlinear differential equations. Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved. If the transformation u= C v is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found. In order to illustrate this approach, several examples about the transformation C are given.

关 键 词：非线性微分方程 变换 算法 解析解 显式格式 

分 类 号：O241.81[理学—计算数学] O175.14[理学—数学]