An asymptotic-numerical hybrid method for solving singularly perturbed linear delay differential equations
type: Item
instance of: scholarly article
title: An asymptotic-numerical hybrid method for solving singularly perturbed linear delay differential equations
zbMATH Open document ID: 1487.65082
DOI: 10.1155/2017/7269450
author: Süleyman Cengizci
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called successive complementary expansion method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show the efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 34K26
zbMATH DE Number: 6915940
Wikidata QID: Q59144298
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/7269450
OpenAlex ID: W2587056380
cites work: Methods for solving singular perturbation problems arising in science and engineering
cites work: A review on singularly perturbed differential equations with turning points and interior layers
cites work: Q3997900
cites work: Q4264396
cites work: Matched asymptotic expansions. Ideas and techniques
cites work: Multiple scale and singular perturbation methods
cites work: Applied Delay Differential Equations
cites work: Q3265851
cites work: Ordinary and delay differential equations
cites work: Differential-difference equations
cites work: Forward and backward continuation for neutral functional differential equations
cites work: A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations
cites work: A finite difference method for singularly perturbed differential-difference equations with layer and oscillatory behavior
cites work: Robust approximation of singularly perturbed delay differential equations by the \(hp\) finite element method
cites work: On discontinuous Galerkin finite element method for singularly perturbed delay differential equations
cites work: Solution of delay differential equations via a homotopy perturbation method
cites work: Solving delay differential equations by an accurate method with interpolation
cites work: Improved reproducing kernel method for singularly perturbed differential-difference equations with boundary layer behavior
cites work: Fitted mesh \(B\)-spline collocation method for singularly perturbed differential-difference equations with small delay
cites work: Spline collocation methods for solving delay-differential equations.
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: Uniformly valid approximation for singular perturbation problems and matching principle
cites work: Q3853988
cites work: Global interactive boundary layer (GIBL) for a channel
description: scientific article; zbMATH DE number 6915940