求解非线性方程的一种线化和校正方法

何吉欢

求解非线性方程的一种线化和校正方法

何吉欢

上海大学, 上海市应用数学和力学研究所, 上海, 200072

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
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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

Linearization and Correction Method for Nonlinear Problems

HE Ji-huan

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

摘要

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。
- 非线性 /
- 近似解 /
- 摄动理论
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

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参考文献(13)

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