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Numerical Methods for Singular Perturbation Problems [PDF]
, 1981 Consider the two-point boundary value problem for a stiff system of ordinary differential equations.
Kreiss, Barbro, Kreiss, Heinz-Otto
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Singular Perturbation on a Subdomain
Journal of Mathematical Analysis and Applications, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G Aguilar, F Lisbona
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Singular perturbations and scaling
Discrete & Continuous Dynamical Systems - B, 2020 Scaling transformations involving a small parameter ({\em degenerate scalings}) are frequently used for ordinary differential equations that model (bio-) chemical reaction networks. They are motivated by quasi-steady state (QSS) of certain chemical species, and ideally lead to slow-fast systems for singular perturbation reductions, in the sense of ...
Sebastian Walcher, Christian Lax
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Supersymmetry and singular perturbations
Journal of Functional Analysis, 1985 Supersymmetric quantum theory (SSQT) is considered in view of perturbation theory. It is first shown in an abstract framework that SSQT may give rise to very singular perturbations, which make perturbation theories for eigenvalues (typically ground state energies) of the Hamiltonians or possibly for other quantities invalid.
Asao Arai, Asao Arai
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On the Singular Perturbations for Fractional Differential Equation
The Scientific World Journal, 2014 The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the
Abdon Atangana
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Perturbation determinants for singular perturbations
Russian Journal of Mathematical Physics, 2014 For proper extensions of a densely defined closed symmetric operator with trace class resolvent difference the perturbation determinant is studied in the framework of boundary triplet approach to extension theory.
Malamud, Mark M., Neidhardt, Hagen
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Aircraft longitudinal decoupling based on a singular perturbation approach
Advances in Mechanical Engineering, 2017 Aircraft longitudinal dynamics is approximated by short-time mode and phugoid mode from experience. In this article, a rigorous mathematical method is provided based on the singular perturbation theory to deal with this decoupling problem.
Shangqiu Shan, Zhongxi Hou, Wenkai Wang
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Singular Perturbations in Viscoelasticity
Rocky Mountain Journal of Mathematics, 1993 We study the singular perturbation for a class of partial integro- differential equations in viscoelasticity of the form \[ \rho u^ \rho_{tt} (t,x) = Eu^ \rho_{xx} (t,x) + \int ^ t _{-\infty} a (t-s) u^ \rho_{xx} (s,x) ds + \rho g (t,x) + f (x),\tag{a} \] when the density \(\rho\) of the material goes to zero. We will prove that when \(\rho \to 0\) the
Grimmer, Ronald, Liu, Hetao
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The peaking phenomenon and singular perturbations [PDF]
Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, 2008 We study the asymptotic behaviour, when the parameter " tends to 0, of a class of singularly perturbed triangular systems x˙ = f(x, y), y˙ = G(y, "). We assume that all solutions of the second equation tend to zero arbitrarily fast when " tends to 0. We assume that the origin of equation x˙ = f(x, 0) is globally asymptotically stable.
Lobry, Claude, Sari, Tewfik
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Parametric Borel summability for some semilinear system of partial differential equations [PDF]
Opuscula Mathematica, 2015 In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \(n\) independent variables. In [Singular perturbation of linear systems with a regular singularity,
Hiroshi Yamazawa, Masafumi Yoshino
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