Averaging method in multipoint problems of the theory of nonlinear oscillations

1996 ◽  
Vol 48 (8) ◽  
pp. 1241-1250
Author(s):  
A. M. Samoilenko ◽  
Ya. R. Petryshyn
Keyword(s):  
Averaging Method ◽  
Nonlinear Oscillations

scholarly journals Investigation of high order stochastic differential equations using averaging method

2007 ◽  
Vol 29 (3) ◽  
pp. 249-255
Author(s):  
Nguyen Dong Anh ◽  
Ngo Thi Hong Hue
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Oscillation ◽  
Colored Noise ◽  
Averaging Method ◽  
Nonlinear Oscillations ◽  
High Order ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stochastic Problems

The averaging method is a useful tool for investigating both deterministic and stochastic quasilinear system. In the stochastic problems, however, the method has often been developed only for mechanical systems subjected to white noise excitations.In the paper this method is applied to high order stochastic differential equations. The nonlinear oscillations in high order deterministic differential equations were investigated in the fundamental work of Prof. Nguyen Van Dao. As an application of high order stochastic differential equations the nonlinear oscillation of single degree of freedom systems subjected to the excitation of a class of colored noises is outlined. The results obtained show that the higher order averaging method can also be successfully extended to the cases of colored noise excitation.

MULTIPLE-SCALE AND NUMERICAL ANALYSES FOR THE NONLINEAR OSCILLATIONS OF A GAS BUBBLE SURROUNDED BY A MAXWELL'S FLUID

2019 ◽  
Vol 46 (3) ◽  
pp. 261-275
Author(s):  
César Yepes ◽  
Jorge Naude ◽  
Federico Mendez ◽  
Margarita Navarrete ◽  
Fátima Moumtadi
Keyword(s):  
Nonlinear Oscillations ◽  
Multiple Scale ◽  
Numerical Analyses ◽  
Gas Bubble

On the solvability of the degenerate Noetherian difference-algebraic boundary value problem

2019 ◽  
Vol 33 ◽  
pp. 204-217
Author(s):  
Sergei Chuiko ◽  
Yaroslav Kalinichenko ◽  
Nikita Popov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Nonlinear Oscillations ◽  
Bounded Operator ◽  
Boundary Value ◽  
Homogeneous Part ◽  
Solvability Conditions ◽  
Engineering Control ◽  
Generalized Green Operator

The original conditions of solvability and the scheme of finding solutions of a linear Noetherian difference-algebraic boundary-value problem are proposed in the article, while the technique of pseudoinversion of matrices by Moore-Penrose is substantially used. The problem posed in the article continues to study the conditions for solvability of linear Noetherian boundary value problems given in the monographs of A.M. Samoilenko, A.V. Azbelev, V.P. Maximov, L.F. Rakhmatullina and A.A. Boichuk. The study of differential-algebraic boundary-value problems is closely related to the investigation of boundary-value problems for difference equations, initiated in the works of A.A. Markov, S.N. Bernstein, Y.S. Bezikovych, O.O. Gelfond, S.L. Sobolev, V.S. Ryabenkyi, V.B. Demidovych, A. Halanai, G.I. Marchuk, A.A. Samarskyi, Yu.A. Mytropolskyi, D.I. Martyniuk, G.M. Vainiko, A.M. Samoilenko and A.A. Boichuk. On the other hand, the study of boundary-value problems for difference equations is related to the study of differential-algebraic boundary-value problems initiated in the papers of K. Weierstrass, N.N. Lusin and F.R. Gantmacher. Systematic study of differential-algebraic boundary value problems is devoted to the works of S. Campbell, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, N.A. Perestiyk, V.P. Yakovets, A.A. Boichuk, A. Ilchmann and T. Reis. The study of differential-algebraic boundary value problems is also associated with numerous applications of such problems in the theory of nonlinear oscillations, in mechanics, biology, radio engineering, control theory, motion stability theory. The general case of a linear bounded operator corresponding to the homogeneous part of a linear Noetherian difference-algebraic boundary value problem has no inverse is investigated. The generalized Green operator of a linear difference-algebraic boundary value problem is constructed in the article. The relevance of the study of solvability conditions, as well as finding solutions of linear Noetherian difference-algebraic boundary-value problems, is associated with the widespread use of difference-algebraic boundary-value problems obtained by linearizing nonlinear Noetherian boundary-value problems for systems of ordinary differential and difference equations. Solvability conditions are proposed, as well as the scheme of finding solutions of linear Noetherian difference-algebraic boundary value problems are illustrated in detail in the examples.

Nonlinear Oscillations of a Chain of Masses in a Liquid

2020 ◽  
Vol 65 (7) ◽  
pp. 238-241
Author(s):  
O. V. Rudenko
Keyword(s):  
Nonlinear Oscillations ◽  
A Chain

scholarly journals Fourt-order nonlinear oscillations of difference equations

2001 ◽  
Vol 42 (3-5) ◽  
pp. 357-368 ◽  
Author(s):  
E. Thandapani ◽  
I.M. Arockiasamy
Keyword(s):  
Difference Equations ◽  
Nonlinear Oscillations
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