Results 261 to 270 of about 66,767 (293)

Singularly Perturbed Ordinary Differential Equations with Nonautonomous Fast Dynamics

Journal of Dynamics and Differential Equations, 1999
The author considers the Cauchy problem \[ \begin{alignedat}{2} \frac{dx}{dt}&=f(x,y),\qquad& x(0)&=x_0, \\ \varepsilon\frac{dy}{dt}&=g(x,y,\frac{t}{\varepsilon}),\qquad& y(0)&=y_0, \end{alignedat} \tag{1} \] with \(x\in {\mathbb{R}}^n\), \(y\in {\mathbb{R}}^m\) and \(t\in[0,1]\). In the Levinson-Tichonov theory, a basic assumption is that solutions to
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A Tau Method with Perturbed Boundary Conditions for Certain Ordinary Differential Equations

Numerical Algorithms, 2005
The author introduces a new form of the tau method in which not only the differential equations are perturbed in order to obtain a polynomial solution but also the initial conditions are simultaneoulsy perturbed. The advantages of the new method and its accuracy in terms of perturbations and errors are studied.
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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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Melnikov functions for singularly perturbed ordinary differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1992
The author studies the homoclinic and periodic orbits for a system of singularly perturbed equations of the form \(\varepsilon y'=g(x,y)+\varepsilon f_ 1(x,y,t)\), \(x'=f_ 0(x,y)+\varepsilon f_ 3(x,y,t)\), \(y\in R^ m\), \(x\in R^ n\), where \(f_ 1\), \(f_ 3\) are \(T\)-periodic in \(t\), and \(g(x,0)=0\).
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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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Periodic Perturbations of a Class of Functional Differential Equations

Journal of Dynamics and Differential Equations, 2021
Marco Spadini
exaly  

SINGULAR PERTURBATION FOR DISCONTINUOUS ORDINARY DIFFERENTIAL EQUATIONS

Symmetry and Perturbation Theory, 2007
M. A. TEIXEIRA, P. R. DA SILVA
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Ordinary differential equations involving perturbations in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1983
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Stability of functional differential equations with variable impulsive perturbations via generalized ordinary differential equations

Bulletin Des Sciences Mathematiques, 2013
S M Afonso, E M Bonotto, M Federson
exaly  

Singular perturbations of difference methods for linear ordinary differential equations

Applicable Analysis, 1980
Hans-Jürgen Reinhardt, G C Hsiao
exaly