δ-摄动方法的一点注释

何吉欢

δ-摄动方法的一点注释

何吉欢

上海大学, 上海市应用数学和力学研究所, 上海, 200072

基金项目: 中国科学院力学研究所非线性国家重点实验(LNM)室资助项目

详细信息

作者简介:
何吉欢(1965- ),男,浙江诸暨人,教授,博士,下列两个国际杂志的主编:International Journal of Nonlinear Sciences and Numerical Simulation(英国Freund出版公司)和International Journal of Nonlinear Modelling in Science and Engineering(英国剑桥国际出版公司)(E-mail:jhhe@mail.shu.edu.cn).

中图分类号: O242.2
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出版历程
- 收稿日期: 2001-01-08
- 修回日期: 2002-01-25
- 刊出日期: 2002-06-15

A Note on Delta-Perturbation Expansion Method

HE Ji-huan

LNM, Institute of Mechanics, Chinese Academy of Sciences; Shanghai Institute of Applied Mathematics and Mechancis, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 研究了最近发展起来的一种新的δ-摄动方法。在这种方法里把非线性项转化为含人工参数δ的形式(如u³转化为v),然后把人工参数作为摄动参数。指出了这种方法有好多优点,但也有很多局限性。该文认为何吉欢提出的线化摄动方法可以很好地克服其存在的局限性。
- 摄动方法 /
- 人工参数 /
- 非线性方程 /
- 同伦方法
Abstract: The Delta-perturbation expansion method,a kind of new perturbation technique depending upon an artificial parameter Delta was studied.The study reveals that the method exits some advantages,but also exits some limitations.To overcome the limitations,the so-called linearized perturbation method proposed by HE Ji-huan can be powerfully applied.
- perturbation method /
- artificial parameter /
- nonlinear equation /
- homotopy

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参考文献(13)

[1]	Bender C M, Pinsky K S, Simmons L M. A new perturbative approach to nonlinear problems[J]. J Math Phys,1989,30(7):1447-1455.
[2]	Awrejcewicz J, Andrianov I V, Manevitch L I. Asymptotic Approaches in Nonlinear Dynamics: New Trends and Applications[M]. Heidelberg: Springer,1998.
[3]	HE Ji-huan. Homotopy perturbation technique[J]. Computer Methods in Applied Mechanics and Engineering,1999,178(3/4):257-262.
[4]	HE Ji-huan. A coupling method of homotopy technique and perturbation technique for nonlinear problems[J]. Int J Nonl Mech,2000,35(1):37-43.
[5]	HE Ji-huan. A new perturbation technique which is also valid for large parameters[J]. Journal of Sound and Vibration,2000,229(5):1257-1263.
[6]	HE Ji-huan. A review on some new recently developed nonlinear analytical techniques[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(1):51-70.
[7]	Andrianov I, Awrejcewicz J. Construction of periodic solution to partial differential equations with nonlinear boundary conditions[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(4):327-332.
[8]	HE Ji-huan. Iteration perturbation method for strongly nonlinear oscillations[J]. Journal of Vibration and Control,2001,7(5):631-642.
[9]	Acton J R, Squire P T. Solving Equations With Physical Understanding[M]. Bristol and Boston: Adam Hilger Ltd,1985.
[10]	HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅰ: expansion of a constant[J]. International Journal of Non-Linear Mechanics,2002,37(2):309-314.
[11]	HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅱ: a new transformation[J]. International Journal of Non-Linear Mechanics,2002,37(2):315-320.
[12]	HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅲ: double series expansion[J]. International Journal of Non-Linear Science and Numerical Simulation,2001,2(4):317-320.
[13]	HE Hi-huan. Bookkeeping parameter in perturbation methods[J]. International Journal of Non-Linear Science and Numerical Simulation,2001,2(3):257-264.