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 …

A numerical approach for singularly perturbed reaction diffusion type volterra-fredholm integro-differential equations

ME Durmaz - Journal of Applied Mathematics and Computing, 2023 - Springer
The goal of this study is to introduce a second-order computational method to solve Volterra-
Fredholm integro-differential equations involving boundary layers. To solve numerically, we …

Exponentially Fitted Finite Difference Approximation for Singularly Perturbed Fredholm Integro-Differential Equation

M Alam, RK Pandey - arXiv preprint arXiv:2401.16379, 2024 - arxiv.org
In this paper, we concentrate on solving second-order singularly perturbed Fredholm integro-
differential equations (SPFIDEs). It is well known that solving these equations analytically is …

A numerical solution of singularly perturbed Fredholm integro-differential equation with discontinuous source term

AS Rathore, V Shanthi - Journal of Computational and Applied …, 2024 - Elsevier
In this paper, we investigate a singularly perturbed Fredholm integro-differential problem
with a discontinuous source term, leading to the formation of interior layers in the solution at …

Numerical solution of Volterra–Fredholm integral equation systems by operational matrices of integration based on Bernstein multi-scaling polynomials

AR Yaghoobnia, R Ezzati - Computational and Applied Mathematics, 2022 - Springer
This paper introduces a new method which is used to obtain numerical solutions of Volterra–
Fredholm linear integral equation systems. In the proposed method, the functions and …

[PDF][PDF] A robust adaptive grid method for first-order nonlinear singularly perturbed Fredholm integro-differential equations.

Z Mao, D Luo - Networks Heterog. Media, 2023 - aimspress.com
In this paper, a robust adaptive grid method is developed for solving first-order nonlinear
singularly perturbed Fredholm integro-differential equations (SPFIDEs). Firstly such …

A fully discrete scheme on piecewise-equidistant mesh for singularly perturbed delay integro-differential equations

M Cakir, B Gunes - Quaestiones Mathematicae, 2024 - Taylor & Francis
This paper chiefly takes into account the singularly perturbed delay Volterra-Fredholm
integro-differential equations by numerically. In this context, firstly, priori estimates are given …

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 …

A Robust Numerical Method for a Singularly Perturbed Semilinear Problem with Integral Boundary Conditions

Z Temel, M Çakır - Contemporary Mathematics (Singapore), 2024 - avesis.yyu.edu.tr
In the present study, we provide an efficient numerical approach for solving singularly
perturbed nonlinear ordinary differential equations with two integral boundary conditions …

A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition

B Gunes, M Cakir - Ukrainian Mathematical Journal, 2024 - Springer
We consider a novel numerical approach for solving boundary-value problems for the
second-order Volterra-Fredholm integrodifferential equation with layer behavior and an …