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Zbl 1102.34039
He, Ji-Huan
Some asymptotic methods for strongly nonlinear equations. (English)
[J] Int. J. Mod. Phys. B 20, No. 10, 1141-1199 (2006). ISSN 0217-9792

The purpose of this survey paper is to discuss recent developments in asymptotic methods for solving both weakly and strongly nonlinear differential equations. In particular, variational approaches, asymptotic expansions in a small parameter, parametrized perturbation, homotopy perturbation, iteration perturbation methods are reviewed and appropriate illustrative examples are considered. The paper is finished with an interesting historical overview of ancient Chinese numerical methods which are not-so-well-known to the mathematical community outside China.
[Svitlana P. Rogovchenko (Famagusta)]

MSC 2000:: *34E10 Asymptotic perturbations (ODE)
34A34 Nonlinear ODE and systems, general
34E05 Asymptotic expansions (ODE)
34E13 Multiple scale methods
49J40 Variational methods including variational inequalities
01A25 Chinese mathematics

Keywords: asymptotic methods; variational methods; parameter-expanding methods; homotopy perturbation method; ancient Chinese numerical methods

Cited in: Zbl 1228.65110 Zbl 1197.35014 Zbl 1189.65233 Zbl 1182.65107 Zbl 1176.65083 Zbl 1162.65397 Zbl 1153.65104 Zbl 1153.65105 Zbl 1147.65079 Zbl 1147.65082 Zbl 1142.65055 Zbl 1152.65470 Zbl 1139.65051 Zbl 1120.65112

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