| 获得非线性微分方程显式解析解的两种新算法 |
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| 引用本文： | 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[J]. 应用数学和力学, 2000, 21(12): 1285-1292 |
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| 作者姓名： | 张鸿庆 闫振亚 |
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| 作者单位： | 大连理工大学应用数学系, 大连116024 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 非线性微分方程 变换 算法 解析解 |
| 收稿时间： | 2000-01-14 |
| 修稿时间： | 2000_01_14 |
Two Types of New Algorithms for Finding Explicit Analytical Solutions of NonlinearDifferential Equations |
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| ZHANG Hong-qing,YAN Zhen-ya. Two Types of New Algorithms for Finding Explicit Analytical Solutions of NonlinearDifferential Equations[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1285-1292 |
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| Authors: | ZHANG Hong-qing YAN Zhen-ya |
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| Affiliation: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P R China |
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| 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. |
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| Keywords: | nonlinear differential equations transformation algorithm analytical solut |
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