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.
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References
LIU Gao-lian. New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique[A]. In: CHENG Chang-jun, DAI Shi-qiang, LIU Yu-lu Eds.Conf of 7th Modern Mathematics and Mechanics[C]. Shanghai: Shanghai University Press, 1997, 47–53. (in Chinese)
HE Ji-huan. Homotopy perturbation technique[J].Computer Methods in Applied Mechanics and Engineering, 1999,178(3/4):257–262.
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.
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.
HE Ji-huan. Modified straightforward expansion[J].Meccanica, 1999,34(4):287–289.
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.
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.
Nayfeh A H.Introduction to Perturbation Techniques[M]. London: John Wiley & Sons, 1981.
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.
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.
HE Ji-huan. Variational iteration method — a kind of nonlinear analytical technique: some examples [J].Int J Nonlinear Mechanics, 1999,34(4):699–708.
Mickens R E.An Introduction to Nonlinear Oscillations[M]. Cambridge: Cambridge University Press, 1981.
Hagedorn P.Nonlinear Oscillations[M]. Wolfram Stafler, transl. Oxford: Clarendon Press, 1981. (English version)
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Contributed by HE Ji-huan
Biography: HE Ji-huan (1965-), Professor, Doctor; Editor-in-chief of International Journal of Nonlinear Sciences and Numerical Simulation (Freund Publishing House Ltd, UK), and International Journal of Nonlinear Modelling in Science and Engineering (Cambridge International Science Publishing, UK)
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Ji-huan, H. Linearization and correction method for nonlinear problems. Appl Math Mech 23, 241–248 (2002). https://doi.org/10.1007/BF02438331
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DOI: https://doi.org/10.1007/BF02438331