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Saddle-node bifurcation of viscous profiles.
Achleitner F, Szmolyan P.
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27th Annual Computational Neuroscience Meeting (CNS*2018): Part Two. [PDF]
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Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE
Applied Numerical Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Satpal Singh +2 more
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Singularly perturbed nonlinear ODEs and interior point optimization algorithms
Proceedings of 1995 American Control Conference - ACC'95, 2005This paper explores the continuous realizations of iterative processes emanating from interior point optimization algorithms, and their connection with nonlinear singularly-perturbed ordinary differential equations. This mathematical connection provides a theoretical framework for the analysis of the dynamical properties long known and exploited in ...
Ezzine, J., Ben-Daya, M.
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Dichotomies and stability in singularly perturbed systems of O.D.E.
Nonlinear Analysis: Theory, Methods & Applications, 1987The authors consider the singularly perturbed initial value problem \((1.1a)\quad \dot x=F(t,x,y,\epsilon),\) \(x(0)=x^ 0\), \((1.1b)\quad \epsilon \dot y=G(t,x,y,\epsilon),\) \(y(0)=y^ 0\), where \(x,F\in {\mathbb{R}}^ n\) and \(y,G\in {\mathbb{R}}^ m\).
Battelli, Flaviano, Lazzari, Claudio
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A Parameter-Uniform Tailored Finite Point Method for Singularly Perturbed Linear ODE Systems
Journal of Computational Mathematics, 2013In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes.
Houde Han, J.J.H. Miller null, Min Tang
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Applications of Mathematics, 2019
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Liu, Chein-Shan, Li, Botong
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Liu, Chein-Shan, Li, Botong
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On singularly perturbed systems of ODE with a multiple root of the degenerate equation
Izvestiya: Mathematics, 2020Abstract We consider a boundary-value problem for a system of two second-order ODE with distinct powers of a small parameter at the second derivative in the first and second equations. When one of the two equations of the degenerate system has a double root, the asymptotic behaviour of the boundary-layer solution of the boundary-value
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