A fitted operator finite difference approximation for singularly perturbed Volterra–Fredholm integro-differential equations

M Cakir, B Gunes - Mathematics, 2022 - mdpi.com
This paper presents a ε-uniform and reliable numerical scheme to solve second-order
singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of …

An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

ME Durmaz, I Amirali, GM Amiraliyev - Journal of Applied Mathematics and …, 2023 - Springer
In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem
with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference …

Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations

M Cakir, B Gunes - Georgian Mathematical Journal, 2022 - degruyter.com
In this study, singularly perturbed mixed integro-differential equations (SPMIDEs) are taken
into account. First, the asymptotic behavior of the solution is investigated. Then, by using …

A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method

MS Hogeme, MM Woldaregay, L Rathour… - Journal of Computational …, 2024 - Elsevier
This paper implemented a stable numerical scheme for solving singularly perturbed linear
second-order Fredholm integro-differential equation. A parameter-uniform numerical method …

Solving singularly perturbed fredholm integro-differential equation using exact finite difference method

SR Badeye, MM Woldaregay, TG Dinka - BMC Research Notes, 2023 - Springer
Objectives In this paper, a numerical scheme is designed for solving singularly perturbed
Fredholm integro-differential equation. The scheme is constructed via the exact (non …

A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

M Çakır, B Güneş - Hacettepe Journal of Mathematics and Statistics, 2022 - dergipark.org.tr
In this research, the finite difference method is used to solve the initial value problem of
linear first order Volterra-Fredholm integro-differential equations with singularity. By using …

A numerical approach for solving nonlinear Fredholm integro-differential equation with boundary layer

M Cakir, Y Ekinci, E Cimen - Computational and Applied Mathematics, 2022 - Springer
The study deals with an initial-value problem for a singularly perturbed nonlinear Fredholm
integro-differential equation. Parameter explicit theoretical bounds on the continuous …

Wavelet-based approximation with nonstandard finite difference scheme for singularly perturbed partial integrodifferential equations

D Kumar, K Deswal, S Singh - Computational and Applied Mathematics, 2022 - Springer
A non-standard finite difference scheme with Haar wavelet basis functions is constructed for
the convection–diffusion type singularly perturbed partial integrodifferential equations. The …

A Parameter‐Uniform Numerical Scheme for Solving Singularly Perturbed Parabolic Reaction‐Diffusion Problems with Delay in the Spatial Variable

AH Ejere, GF Duressa… - … of Mathematics and …, 2023 - Wiley Online Library
The objective of this research work is to develop and analyse a numerical scheme for
solving singularly perturbed parabolic reaction‐diffusion problems with large spatial delay …

[HTML][HTML] Numerical analysis for second order differential equation of reaction-diffusion problems in viscoelasticity

S Elango, L Govindarao, J Mohapatra, R Vadivel… - Alexandria Engineering …, 2024 - Elsevier
This study uses numerical methods to solve a specific type of reaction-diffusion problem
arising in viscoelasticity (singularly perturbed Fredholm integro-differential equations) …