A recent survey on computational techniques for solving singularly perturbed boundary value problems

M Kumar, P Singh, HK Mishra - International Journal of Computer …, 2007 - Taylor & Francis
This survey paper contains a surprisingly large amount of material and indeed can serve as
an introduction to some of ideas and methods of singular perturbation theory. In continuation …

Numerical solution of singularly perturbed Fredholm integro-differential equations by homogeneous second order difference method

ME Durmaz, M Cakir, I Amirali, GM Amiraliyev - Journal Of Computational …, 2022 - Elsevier
This work presents a computational approximate to solve singularly perturbed Fredholm
integro-differential equation with the reduced second type Fredholm equation. This problem …

A finite difference method for the singularly perturbed problem with nonlocal boundary condition

M Cakir, GM Amiraliyev - Applied mathematics and computation, 2005 - Elsevier
The purpose of this paper is to present a finite difference method for numerical solutions of
singularly perturbed boundary value problem for second order ordinary differential equation …

Numerical solution of a singularly perturbed three-point boundary value problem

M Cakir, GM Amiraliyev - International Journal of Computer …, 2007 - Taylor & Francis
We consider a uniform finite difference method on an S-mesh (Shishkin type mesh) for a
singularly perturbed semilinear one-dimensional convection–diffusion three-point boundary …

[PDF][PDF] Uniform second-order difference method for a singularly perturbed three-point boundary value problem

M Cakır - Advances in Difference Equations, 2010 - Springer
We consider a singularly perturbed one-dimensional convection-diffusion three-point
boundary value problem with zeroth-order reduced equation. The monotone operator is …

A uniformly convergent difference method for the periodical boundary value problem

GM Amiraliyev, H Duru - Computers & Mathematics with Applications, 2003 - Elsevier
The periodical boundary value problem for linear second-order ordinary differential equation
with small parameter by the first and second derivatives is considered. By the method of …

[HTML][HTML] A numerical method for nonlinear singularly perturbed multi-point boundary value problem

M Çakır, D Arslan - Journal of Applied Mathematics and Physics, 2016 - scirp.org
We consider a uniform finite difference method for nonlinear singularly perturbed multi-point
boundary value problem on Shishkin mesh. The problem is discretized using integral …

A computational approach to solving a second-order singularly perturbed Fredholm integro-differential equation with discontinuous source term

WS Manebo, MM Woldaregay, TG Dinka… - Numerical …, 2024 - Springer
This article introduces a numerical method to solve a singularly perturbed Fredholm integro-
differential equation of second order with a discontinuous source term. To effectively handle …

A uniformly convergent numerical method for singularly perturbed semilinear integro-differential equations with two integral boundary conditions

B Gunes, M Cakir - Computational Mathematics and Mathematical Physics, 2023 - Springer
This paper purposes to present a new discrete scheme for the singularly perturbed
semilinear Volterra–Fredholm integro-differential equation including two integral boundary …

An approximate solution of singularly perturbed problem on uniform mesh

D Arslan, E Çelik - An International Journal of Optimization and Control …, 2024 - ijocta.org
In this study, we obtain approximate solution for singularly perturbed problem of differential
equation having two integral boundary conditions. With this purpose, we propose a new …