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Perturbation Formulas for a Nonlinear Eigenvalue Problem for Ordinary Differential Equations

Computational Mathematics and Mathematical Physics, 2018
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Abramov, A. A., Yukhno, L. F.
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Singularly perturbed ordinary differential equations with dynamic limits

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1996
Coupled slow and fast motions generated by ordinary differential equations are examined. The qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after. Invariant measures of the parametrised fast flow are employed to describe the limit behaviour, rather than algebraic equations which are used in the standard ...
Artstein, Zvi, Vigodner, Alexander
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Singular perturbation problems of ordinary differential equations

1968
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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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On a Perturbation in a Two-Parameter Ordinary Differential Equation of the Second Order

Canadian Mathematical Bulletin, 1971
Let us consider the linear system in the two parameters λ and μ; i. e.,1.11.2and where for the moment we shall assume both b(x) and q(x) are real-valued, continuous functions in [0, 1].
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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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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 a Perturbation Theory and on Strong Convergence Rates for Stochastic Ordinary and Partial Differential Equations With Nonglobally Monotone Coefficients

Annals of Probability, 2020
Arnulf Jentzen, Martin Hutzenthaler
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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