A brief survey on numerical methods for solving singularly perturbed problems

MK Kadalbajoo, V Gupta - Applied mathematics and computation, 2010 - Elsevier
In the present paper, a brief survey on computational techniques for the different classes of
singularly perturbed problems is given. This survey is a continuation of work performed …

An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh

P Das - Numerical Algorithms, 2019 - Springer
The present work considers a nonlinear system of singularly perturbed delay differential
equation whose each component of the solution has multiple layers. Here, we provide an a …

[HTML][HTML] Modified reproducing kernel method for singularly perturbed boundary value problems with a delay

FZ Geng, SP Qian - Applied Mathematical Modelling, 2015 - Elsevier
This paper is devoted to the numerical treatment of a class of singularly perturbed delay
boundary value problems with a left layer. The method is proposed based on the …

[HTML][HTML] A finite-difference method for a singularly perturbed delay integro-differential equation

M Kudu, I Amirali, GM Amiraliyev - Journal of Computational and Applied …, 2016 - Elsevier
We consider the singularly perturbed initial value problem for a linear first order Volterra
integro-differential equation with delay. Our purpose is to construct and analyse a numerical …

A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

F Erdogan, MG Sakar, O Saldır - Applied Mathematics and Nonlinear …, 2020 - sciendo.com
The purpose of this paper is to present a uniform finite difference method for numerical
solution of a initial value problem for semilinear second order singularly perturbed delay …

Parameter-robust numerical scheme for time-dependent singularly perturbed reaction–diffusion problem with large delay

K Bansal, KK Sharma - Numerical Functional Analysis and …, 2018 - Taylor & Francis
This work presents the development of numerical scheme for second-order time-dependent
singularly perturbed reaction-diffusion problem with large delay in the undifferentiated term …

[HTML][HTML] Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay

Ö Yapman, GM Amiraliyev, I Amirali - Journal of Computational and …, 2019 - Elsevier
In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra
integro-differential equation was considered. By the method of integral identities with the use …

Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method

S Nicaise, C Xenophontos - Computational Methods in Applied …, 2013 - degruyter.com
We consider the finite element approximation of the solution to a singularly perturbed
second order differential equation with a constant delay. The boundary value problem can …

[PDF][PDF] Piecewise reproducing kernel-based symmetric collocation approach for linear stationary singularly perturbed problems

FZ Geng - AIMS Math, 2020 - aimspress.com
Piecewise reproducing kernel-based symmetric collocation approach for linear stationary
singularly perturbed problems Page 1 http://www.aimspress.com/journal/Math AIMS …

A fitted approximate method for a Volterra delay-integro-differential equation with initial layer

GM Amiraliyev, Ö Yapman, M Kudu - Hacettepe Journal of …, 2019 - dergipark.org.tr
This study is concerned with the finite-difference solution of singularly perturbed initial value
problem for a linear first order Volterra integro-differential equation with delay. The method is …