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Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

International Journal of Computer Mathematics, 2015
In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter.
Pratibhamoy Das, Srinivasan Natesan
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Dichotomies and stability in singularly perturbed systems of O.D.E.

Nonlinear Analysis: Theory, Methods & Applications, 1987
The 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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Singularly perturbed nonlinear ODEs and interior point optimization algorithms

Proceedings of 1995 American Control Conference - ACC'95, 2005
This 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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A Parameter-Uniform Tailored Finite Point Method for Singularly Perturbed Linear ODE Systems

Journal of Computational Mathematics, 2013
In 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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Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions

Applications of Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Chein-Shan, Li, Botong
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Experiments with a local adaptive grid h-refinement for the finite-difference solution of BVPs in singularly perturbed second-order ODEs

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Entirely Exponential-Type Scheme (E2S) for Optimization Problems with Singularly Perturbed ODE Constraints: The Model Problem

Numerical Mathematics: Theory, Methods and Applications
We found that no convergence to the correct solution can happen when a popular method is applied to discretize the derivative appearing in the objective function for optimization problems with singularly perturbed ODE constraints. The non-convergence mentioned above can occur even if the error bound of the numerical solution of the state equation has ...
Mengyu Li, Tiegang Liu, Kui Cao, Chengliang Feng, Bin Zhang, Weixiong Yuan   +5 more
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Adaptive solution of BVPs in singularly perturbed second-order ODEs, by the extended Numerov method combined with an iterative local grid h-refinement

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite-Time Fuzzy Control for Nonlinear Singularly Perturbed Systems With Input Constraints

IEEE Transactions on Fuzzy Systems, 2022
Wei Xing Zheng, Shengyuan Xu
exaly  

Singularly perturbed ODEs with multiple roots of the degenerate equation

Proceeding of the International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin, 2018
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