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Some asymptotic methods for strongly nonlinear equations. (English) Zbl 1102.34039

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.

MSC:

34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34E05 Asymptotic expansions of solutions to ordinary differential equations
34E13 Multiple scale methods for ordinary differential equations
49J40 Variational inequalities
01A25 History of Chinese mathematics
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