获得非线性微分方程显式解析解的两种新算法

张鸿庆; 闫振亚

获得非线性微分方程显式解析解的两种新算法

大连理工大学应用数学系, 大连116024

基金项目: 国家重点基础研究发展规划基金资助项目(G1998030600);教育部博士点基金资助项目(98014119)

详细信息

作者简介:
张鸿庆(1936- ),男,黑龙江人,教授,博士生导师.

中图分类号: O175.29
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出版历程
- 收稿日期: 2000-01-14
- 修回日期: 2000-08-21
- 刊出日期: 2000-12-15

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

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P R China

摘要

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C的表达式。
- 非线性微分方程 /
- 变换 /
- 算法 /
- 解析解
Abstract: The idea of AC=BD was applied to solve the nonlinear differential equations.Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved.If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found.In order to illustrate this approach,several examples about the transformation C are given.
- nonlinear differential equations /
- transformation /
- algorithm /
- analytical solution

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参考文献(19)

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