scholarly journals About Averaging in Hyperbolic Equation under the Influence of Multifrequence Disturbances

2019 ◽  
pp. 9-10
Author(s):  
Yaroslav Bihun ◽  
Ihor Skutar
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Hyperbolic Equation ◽  
Ordinary Differential Equations ◽  
Averaging Method ◽  
Initial Problem

The research deals with the existence of thesolution of the initial problem for hyperbolic equation under themultifrequency disturbances, which are described by the systemof ordinary differential equations (ODE) with multipoint andintegral conditions. The averaging method over fast variables isgrounded and estimation of accuracy of the method whichobviously depends on the small parameter was found.

scholarly journals On the Question of Asymptotic Integration of Singularly Perturbed Fractional-Order Problems

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Burkhan Kalimbetov
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Fractional Order ◽  
Initial Problem ◽  
Singularly Perturbed ◽  
Asymptotic Integration ◽  
Partial Derivatives ◽  
Systems Of Differential Equations ◽  
Regularization Problem ◽  
Iterative Systems

In this paper we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. Regularization problem is produced, and algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given. 

scholarly journals Approximate transformations for van der Pol-type equations

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
R. K. Gazizov ◽  
C. M. Khalique
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Ordinary Differential Equations ◽  
Transformation Groups ◽  
Van Der Pol ◽  
Approximate Symmetries ◽  
Approximate Integration ◽  
Successive Reduction

Classification of van der Pol-type equations with respect to admitted approximate transformation groups transforming a small parameter is given. It is shown that approximate symmetries transforming the small parameter as well as the usual approximate symmetries can be used for approximate integration (e.g., by method of successive reduction of order) of ordinary differential equations with a small parameter.

scholarly journals Averaging for ordinary differential equations perturbed by a small parameter

2016 ◽  
Vol 141 (2) ◽  
pp. 143-151
Author(s):  
Mustapha Lakrib ◽  
Tahar Kherraz ◽  
Amel Bourada
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Ordinary Differential Equations
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