Numerical integration of a class of singularly perturbed delay differential equations with small shift
type: Item
instance of: scholarly article
title: Numerical integration of a class of singularly perturbed delay differential equations with small shift
zbMATH Open document ID: 1269.34081
DOI: 10.1155/2012/572723
author: Gemechis File
author: Y. N. Reddy
published in: International Journal of Differential Equations
publication date: 2013-06-10T00:00:00Z
review text: Summary: We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson's rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter \(\delta\) and the perturbation parameter \(\varepsilon\).
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 34K26
zbMATH DE Number: 6172122
zbMATH Keywords: Simpson's rule
zbMATH Keywords: linear interpolation
Wikidata QID: Q58702816
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/572723
OpenAlex ID: W2117602625
cites work: Heat waves
cites work: State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times
cites work: Formation and propagation of localized states in extended systems
cites work: Fixed points, stability, and exact linearization
cites work: Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays
cites work: Oscillation and Chaos in Physiological Control Systems
cites work: Numerical method for a singularly perturbed convection-diffusion problem with delay
cites work: Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. V. Small Shifts with Layer Behavior
cites work: Singular Perturbation Analysis of Boundary-Value Problems for Differential-Difference Equations. VI. Small Shifts with Rapid Oscillations
cites work: Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations
cites work: A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations
cites work: Numerical analysis of singularly perturbed delay differential equations with layer behavior
cites work: Singular Perturbation Analysis of Boundary Value Problems for Differential‐Difference Equations. IV. A Nonlinear Example with Layer Behavior
cites work: Numerical treatment for singularly perturbed nonlinear differential difference equations with negative shift
cites work: Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
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cites work: Asymptotic analysis and solution of a finite-horizon \(H_{\infty}\) control problem for singularly-perturbed linear systems with small state delay
cites work: A nonasymptotic method for general linear singular perturbation problems
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description: scientific article; zbMATH DE number 6172122