General Solutions of Nonlinear Differential Equations in the Neighbourhood of Quasi-Periodic Solutions

1976 ◽  
pp. 60-87
Author(s):  
N. N. Bogoljubov ◽  
Ju. A. Mitropoliskii ◽  
A. M. Samoilenko
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
General Solutions

scholarly journals A New Approach to Approximate Solutions for Nonlinear Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Safia Meftah
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Small Parameter ◽  
Perturbation Method ◽  
Periodic Solutions ◽  
Asymptotic Expansions ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Approximation Methods ◽  
New Approach

The question discussed in this study concerns one of the most helpful approximation methods, namely, the expansion of a solution of a differential equation in a series in powers of a small parameter. We used the Lindstedt-Poincaré perturbation method to construct a solution closer to uniformly valid asymptotic expansions for periodic solutions of second-order nonlinear differential equations.

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