New periodic solutions of nonautonomous systems of nonlinear differential equations with derivatives multiplied by a small parameter and their stability

2012 ◽  
Vol 85 (1) ◽  
pp. 149-152 ◽  
Author(s):  
M. E. Mazurov
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
Nonautonomous Systems

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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