三阶非线性向量常微分方程边值问题的奇摄动

林苏榕; 倪明康

三阶非线性向量常微分方程边值问题的奇摄动

林苏榕^1,2,
倪明康^2,3

1.
福建广播电视大学计算机系, 福州 350003;
2.
华东师范大学数学系, 上海200062;
3.
上海高校计算科学E-研究院上海交通大学研究所, 上海 200030

详细信息

中图分类号: O175
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出版历程
- 收稿日期: 2011-01-01
- 修回日期: 2011-04-01
- 刊出日期: 2012-01-25

Singular perturbation of BVP for third-order nonlinear VDE

LIN Su-rong^1,2,
NI Ming-Kang^2,3

1.
~ Department of Computer, Fujian Radio and TV University, Fuzhou 350003, China;
2.
~ Department of Mathematics, East China Normal University, Shanghai 200062, China;
3.
~ SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai

摘要

摘要: 研究非线性三阶向量常微分方程的奇摄动边值问题. 在一定的条件下, 转变所给方程为对角化系统, 然后去求解等价的积分方程, 再用逐步逼近法和不动点原理, 证得摄动问题解的存在并给出渐近估计. 最后, 给出了若干应用例子.
- 奇异摄动 /
- 边值问题 /
- 非线性向量微分方程 /
- 对角化方法
Abstract: The singularly perturbations for the vector boundary value problem of nonlinear third-order ordinary differential equations were studied. Under certain conditions, the given differential equation was transformed into a diagonalized system, and then the equivalent integral equations was solved. By using the method of succesive approximation and the theorem of fixed point, the existence of the solution of singular perturbation problem was proved and the asymptotic estimation was obtained. Finally, several examples of application were given.
- singular perturbation /
- boundary value problem /
- nonlinear vector equation /
- diagonalization method

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参考文献(1)

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