Linearization and Correction Method for Nonlinear Problems

HE Ji-huan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(3): 221-228

HE Ji-huan. Linearization and Correction Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 2002, 23(3): 221-228.

Citation:

HE Ji-huan. Linearization and Correction Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 2002, 23(3): 221-228.

Citation:

HE Ji-huan. Linearization and Correction Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 2002, 23(3): 221-228.

PDF( 304 KB)

Linearization and Correction Method for Nonlinear Problems

HE Ji-huan

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

Received Date: 2001-01-08
Rev Recd Date: 2001-08-28
Publish Date: 2002-03-15

Abstract

Abstract

A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques,the present theory does not assume that the solution is expressed in the form of a power series of small parameter.To obtain an asymptotic solution of nonlinear system,the technique first searched for a solution for the linearized system,then a correction was added to the linearized solution.So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
- nonlinearity,
- asymptotic solution,
- perturbation technique

FullText(HTML)

References(13)

References

[1]	刘高联. 奇异摄动理论发展的新方向:人工参数法和反摄动法[A]. 见:程昌钧,戴世强,刘宇陆主编. 现代数学和力学(MMM)Ⅶ[C]. 上海:上海大学出版社,1997,47-53.
[2]	HE Ji-huan. Homotopy perturbation technique[J]. Computer Methods in Applied Mechanics and Engineering,1999,178(3/4):257-262.
[3]	HE Ji-huan. A coupling method of homotopy technique and perturbation technique for nonlinear problems[J]. International J Nonlinear Mechanics,2000,35(1):37-43.
[4]	HE Ji-huan. Some new approach to Duffing equation with strongly & high order nonlinearity (Ⅱ) parameterized perturbation technique[J]. Communications in Nonlinear Science & Numerical Simulation,1999,4(1):81-82.
[5]	HE Ji-huan. Modified straightforward expansion[J]. Meccanica,1999,34(4):287-289.
[6]	HE Ji-huan. A new perturbation technique which is also valid for large parameters[J]. Journal of Sound and Vibration,1999,229(5):1257-1263.
[7]	HE Ji-huan. A review on some new recently developed nonlinear analytical techniques[J]. Int J Nonlinear Sciences & Numerical Simulation,2000,1(1):51-70.
[8]	Nayfeh A H. Introduction to Perturbation Techniques[M]. London: John Wiley & Sons,1981.
[9]	HE Ji-huan. Modified Lindsted-Poincare Methods for some strongly nonlinear oscillations,part Ⅰ: Expansion of a constant[J]. Int J Nonlinear Mechanics,2002,37(2):309-314.
[10]	HE Ji-huan. Modified Lindsted-Poincare Methods for some strongly nonlinear oscillations, part Ⅱ: a new transformation[J]. Int J Nonlinear Mechanics,2002,37(2):315-320.
[11]	HE Ji-huan. Variational iteration method-a kind of nonlinear analytical technique: some examples[J]. Int J Nonlinear Mechanics,1999,34(4):699-708.
[12]	Mickens R E. An Introduction to Nonlinear Oscillations[M]. Cambridge: Cambridge University Press,1981.
[13]	Hagedorn P. Nonlinear Oscillations[M]. Wolfram Stafler,transl.[M]. Oxford: Clarendon Press,1981.(English version)