Results 291 to 300 of about 66,753 (329)

Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

Advances in Applied Mathematics and Mechanics, 2011
AbstractThe paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.
Leonid Berezansky, Michael Gil’, Liora Troib   +2 more
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Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations

Journal of Mathematical Physics, 2009
Lie theory is applied to perturbation problems of ordinary differential equations to construct approximate solutions and invariant manifolds according to the renormalization group approach of Iwasa and Nozaki [“A method to construct asymptotic solutions invariant under the renormalization group,” Prog. Theor. Phys. 116, 605 (2006)].
Chiba, Hayato, Iwasa, Masatomo
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Quasiperiodic Solutions of Functional Singularly Perturbed Linear Ordinary Higher-Order Differential Equations

Journal of Mathematical Sciences, 2020
Consider a system of differential equations \[ \varphi^{(1)}=\omega,\ \ \varepsilon a(\varphi)x^{(n+1)}+x^{(n)}+b_{1}(\varphi)x^{(n-1)}+\ldots+b_{n}(\varphi)x=f(\varphi),\tag{1} \] where \(\varphi \in \mathbb R^{m}\), \(\omega =(\omega_{1},\omega_{2},\ldots,\omega_{m})\) is a frequence basis, \(x\in \mathbb R\), \(f\in \mathcal T^{m}\) and \(\mathcal T^
Er'omenko, V. O., Aliluiko, A. M.
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Non-standard analysis and singular perturbations of ordinary differential equations

Russian Mathematical Surveys, 1984
This is a lively and interesting survey of a lively and interesting area of current research, namely the application of non-standard analysis to singular perturbation problems for ordinary differential equations. In particular, the authors discuss certain singular solutions (called ''ducks'') of nonlinear second-order equations depending on a small ...
Zvonkin, A. K., Shubin, M. A.
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Invariant manifolds of singularly perturbed ordinary differential equations

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1985
Consider an autonomous system \[ (1)\quad dx/dt=f(x,y,\epsilon),\quad \epsilon dy/dt=g(x,y,\epsilon), \] where \(f: D\to {\mathbb{R}}^ m\), \(g: D\to {\mathbb{R}}^ n\), \(D=D_ 1\times D_ 2\times (-\epsilon_ 0,\epsilon_ 0)\) is a bounded domain in \({\mathbb{R}}^{m+n+1}\), and \(D_ 1\) is star shaped with \(C^{\nu +1}\) boundary, \(\nu\geq 1\).
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SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR HIGHER ORDINARY DIFFERENTIAL EQUATION

Acta Mathematica Scientia, 1992
The authors construct the asymptotic expansion of the solution of a singularly perturbed boundary value problem for a quasilinear higher order ordinary differential equation with three small parameters (two singular perturbation parameters in the operator and one in the boundary conditions). The asymptotic method of Vishik and Lyusternik is applied. An
Lin, Zongchi, Lin, Surong
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SINGULAR PERTURBATIONS OF ORDINARY DIFFERENTIAL EQUATIONS

1961
Abstract : A discussion is presented concerning the perturbation method for ordinary differential equations with a small parameter epsilon. As illustrations of this procedure, use of the Neumann series and the Fredholm expansion is made. The solution of the eigenvalue problem is made for an ordinary differential equation as a power series in epsilon.
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Perturbed Taylor expansion for bifurcation of solution of singularly parameterized perturbed ordinary differentia equations and differential algebraic equations

Journal of Education for Pure Science- University of Thi-Qar, 2021
In This paper deals with the study of singularity perturbed ordinary differential equation, and is considered the basis for obtaining the system of differential algebraic equations. In this study the we use implicit function theorem to solve for fast variable y to get a reduced model in terms of slow dynamics locally around x.
Dr.Kamal Hamid Yasser Al-Yassery, Zahraa Hameed Ali Al-Kafaji   +1 more
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A collocation approximation of singularly perturbed second order ordinary differential equation

International Journal of Computer Mathematics, 1991
This paper concerns the numerical solutions of two-point singularly perturbed boundary value problems for second order ordinary differential equations. For the linear problem, Canonical polynomials are constructed as new basis for collocation solution in the smooth region which is superposed with an exponential function in the boundary layer region ...
O. A. Taiwo, P. Onumanyi
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On the Estimation of Small Perturbations in Ordinary Differential Equations

1983
The essential subject of this work is concerned with those problems represented by a system of ordinary differential equations involving one or several small perturbing functions to be determined in order to obtain either a solution given in advance (control problems) or a solution that approximates a set of measurements that may be affected by random ...
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