| 一类非线性微分方程的近似解析解 |
| |
| 引用本文： | 郑连存,冯志丰,张欣欣.一类非线性微分方程的近似解析解[J].物理学报,2007,56(3):1549-1554. |
| |
| 作者姓名： | 郑连存 冯志丰 张欣欣 |
| |
| 作者单位： | (1)北京科技大学机械工程学院,北京 100083; (2)北京科技大学数学力学系，北京 100083 |
| |
| 摘 要： | 从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合，证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题.
关键词：
广义扩散方程
非线性边界值问题
解析拆分
近似解析解
|
| 关 键 词： | 广义扩散方程 非线性边界值问题 解析拆分 近似解析解 |
| 文章编号： | 1000-3290/2007/56(03)/1549-06 |
| 收稿时间： | 2006-06-15 |
| 修稿时间： | 06 15 2006 12:00AM |
Approximate analytical solutions for a class of nonlinear differential equations |
| |
| Zheng Lian-Cun,Feng Zhi-Feng,Zhang Xin-Xin.Approximate analytical solutions for a class of nonlinear differential equations[J].Acta Physica Sinica,2007,56(3):1549-1554. |
| |
| Authors: | Zheng Lian-Cun Feng Zhi-Feng Zhang Xin-Xin |
| |
| Institution: | 1. Department of Mathematics and Mechanics, Being University of Science and Technology, Beijing 100083, China ; 2 .School of Mechanical Engineering, Beijing University of Science and Technology, Beifing 100083, China |
| |
| Abstract: | This paper presents a theoretical analysis for a class of generalized diffusion equations. An effective analytical decomposition and numerical technique is given by similarity transformations and the analytical decomposition technique. The approximate analytical solution may be expressed in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of approximate solutions are illustrated by good agreement with numerical results. |
| |
| Keywords: | diffusion equations nonlinear boundary value problems analytical decomposition approximate solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《物理学报》浏览原始摘要信息 |
| 点击此处可从《物理学报》下载免费的PDF全文 |
