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Class of Perturbation Theories of Ordinary Differential Equations

Journal of Mathematical Physics, 1971
A class of perturbation theories of ordinary differential equations is studied in a systematic and rigorous way. This class contains the perturbation theory by Kruskal [J. Math. Phys. 3, 806 (1962)] and its generalization discussed by Coffey [J. Math. Phys.
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Regular Perturbation of Ordinary Differential Equations

2015
In this chapter we find asymptotic solutions of regularly perturbed equations and systems of equations, to which problems in mechanics are reduced. We consider Cauchy problems, problems for periodic solutions and boundary value problems.
S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt   +4 more
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Asymptotic Stability for Ordinary Differential Equations with Delayed Perturbations

SIAM Journal on Mathematical Analysis, 1974
Asymptotic stability of the zero solution of \[\dot x(t) = - a(t)x(t) + P(t,x_t )\] is studied with a direct method of Razumikhin. If $| {P(t,\varphi )} | \leqq \alpha (t)\theta \| \varphi \|$ for some $\theta 0$, then zero is exponentially stable; if the condition on $a(t)$ is weakened to $a(t) \geqq 0$ and $\int ^\infty a(t)dt = \infty $, then zero
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Singularly Perturbed Linear Ordinary Differential Equations

2015
In this chapter, we study systems of linear differential equations with variable coefficients.
S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt   +4 more
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Exponential methods for singularly perturbed ordinary differential–difference equations

Applied Mathematics and Computation, 2006
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Perturbation Formulas for a Nonlinear Eigenvalue Problem for Ordinary Differential Equations

Computational Mathematics and Mathematical Physics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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Singular perturbation problems of ordinary differential equations

1968
This item was digitized as part of a project to share McGill's intellectual legacy with the public. If you are the copyright holder or a relative of the copyright holder who is deceased, you may request withdrawal by emailing escholarship.library@mcgill.ca.
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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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