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求解非线性方程的一种线化和校正方法

何吉欢

何吉欢. 求解非线性方程的一种线化和校正方法[J]. 应用数学和力学, 2002, 23(3): 221-228.
引用本文: 何吉欢. 求解非线性方程的一种线化和校正方法[J]. 应用数学和力学, 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.

求解非线性方程的一种线化和校正方法

详细信息
    作者简介:

    何吉欢(1965- ),男,浙江诸暨人,教授,博士;任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: O175.14;O322

Linearization and Correction Method for Nonlinear Problems

  • 摘要: 提出了一种拟摄动理论——线化和校正方法。在该理论中,不象传统的摄动方法假设其近似解可表示成小参数的级数形式,而是先把方程线性化,再求其线化方程的解,然后再校正线化方程的解。这样得到的近似解不受方程中的“参数”的影响。
  • [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)
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  • 被引次数: 0
出版历程
  • 收稿日期:  2001-01-08
  • 修回日期:  2001-08-28
  • 刊出日期:  2002-03-15

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