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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.

34E10Perturbations, asymptotics (ODE)
34A34Nonlinear ODE and systems, general
34E05Asymptotic expansions (ODE)
34E13Multiple scale methods (ODE)
49J40Variational methods including variational inequalities
01A25Chinese mathematics
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