Results 151 to 160 of about 594 (186)

On Nonlinear Singularly Perturbed Initial Value Problems

SIAM Review, 1988
The author studies the singular perturbation initial value problem for the nonlinear system \(x'=f(x,y,t,\epsilon),\) \(\epsilon y'=g(x,y,t,\epsilon)\) on a bounded interval \([0,1]\) with smooth vector functions \(f\) and \(g\) of dimensions \(m\) and \(n\) respectively and with prescribed vector function \(x(0),y(0)\).
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Interval Schemes for Singularly Perturbed Initial Value Problems

Reliable Computing, 2005
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Abdelhay A. Salama, Emad Hamdy
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Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems

SIAM Journal on Applied Mathematics, 1993
Summary: Strong localized perturbations of linear and nonlinear eigenvalue problems in a bounded two-dimensional domain \(D\) are considered. The effects on an eigenvalue \(\lambda_ 0\) of the Laplacian, and on the fold point \(\lambda_{c0}\) of a nonlinear eigenvalue problem, of removing a small subdomain \(D_ \varepsilon\), of ``radius ...
Michael Jeffrey Ward, William D. Heshaw, Joseph B. Keller   +2 more
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Singularly perturbed problems in partial differential equations: a survey

Applied Mathematics and Computation, 2003
The authors survey a surprisingly large amount of material on singularly perturbed partial differential equations and which indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory. This paper limits its coverage to some standard singular perturbation models considered by various workers and the methods ...
Mohan K. Kadalbajoo, Kailash C. Patidar
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Nonlinear singularly perturbed problems of ultra parabolic equations

Applied Mathematics and Mechanics, 2008
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Lin, Surong, Mo, Jiaqi
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On Numerical Solution of Singularly Perturbed Optimal Control Problems

Journal of Optimization Theory and Applications, 2017
Singularly perturbed (SP) optimal control problems in which optimal controls may take the form of rapidly oscillating functions, i. e., problems with fast and slow dynamics depending on a parameter \(\varepsilon\), are considered. It is demonstrated that a straightforward application of standard optimal control methods is computationally infeasible for
Vladimir Gaitsgory, Matthias Gerdts
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A CLASS OF SINGULARLY PERTURBED NONLINEAR ROBIN PROBLEMS

Acta Mathematica Scientia, 1994
Summary: Taking the search of steady state solutions of one-dimension reaction- diffusion problems as the background, we study the existence and asymptotic estimates of solutions of the singularly perturbed Robin problem \(a(x, \varepsilon)y''= f(x, y, y', \varepsilon)\), \(a_ 0 y(0, \varepsilon)- b_ 0 y'(0, \varepsilon)= A_ 0\), \(a_ 1 y(1 ...
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Some singular singularly-perturbed problems. II.

1999
Summary: This paper continuous part I published in the previous number of the same volume. For the corresponding summary see [ibid. 15, No. 3, 260--271 (1999; Zbl 0968.34015)].
Chang, K. W., Meng, J.
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Singularly perturbed problems with minimal pulse

Translation from Differ. Uravn. 19, No.2, 259-269 (Russian) (1983; Zbl 0517.49018).
Rozov, N. Kh., Gichev, T. R.
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Hysteresis in Singularly Perturbed Problems

2005
A discontinous hysteresis law is derived as a singular limit in differential equations with non-monotone nonlinearities arising, for example, in a model for instabilities of a fluid flow in a tube with pump and valve with uncertain parameters. The input-output ralation is considered in the space of regulated functions, and it is show that it preserves ...
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