Results 221 to 230 of about 6,287 (263)

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 ...
exaly   +2 more sources

Singularly Perturbed Linear Stochastic Ordinary Differential Equations

SIAM Journal on Mathematical Analysis, 1979
Singularly perturbed linear differential equations with random forcing functions have recently been studied as models of control and filtering systems. The analysis in these studies has been somewhat formal, and important properties of the boundary layer behavior have been neglected as a consequence.
Blankenship, G., Sachs, S.
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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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Some perturbation problems in ordinary differential equations

Funkcialaj Ekvacioj, 1967
The author considers the differential equation \[ x' = f(t,x) + G(t) \] on \(\mathbb R^1\times \mathbb R^n\) where \(R(t,x) + G(t)\) is the perturbing part. It is shown that the existence of a positively bounded and exponentially stable solution is not affected by the perturbing terms if \(R(t,0)=0\), \(\vert R(t,x) - R(t,y)\vert \le k\,\vert x - y ...
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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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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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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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