A review on singularly perturbed differential equations with turning points and interior layers

KK Sharma, P Rai, KC Patidar - Applied Mathematics and computation, 2013 - Elsevier
Singular perturbation problems with turning points arise as mathematical models for various
physical phenomena. The problem with interior turning point represent one-dimensional …

A systematic review on the solution methodology of singularly perturbed differential difference equations

GF Duressa, IT Daba, CT Deressa - Mathematics, 2023 - mdpi.com
This review paper contains computational methods or solution methodologies for singularly
perturbed differential difference equations with negative and/or positive shifts in a spatial …

A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters

V Gupta, MK Kadalbajoo, RK Dubey - International Journal of …, 2019 - Taylor & Francis
In the present paper, a parameter-uniform numerical method is constructed and analysed for
solving one-dimensional singularly perturbed parabolic problems with two small …

Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front

DV Lukyanenko, AA Borzunov… - … in nonlinear science and …, 2021 - Elsevier
An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-
advection equations is proposed. As an example, we consider an inverse problem 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 …

[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 robust numerical method for a singularly perturbed Fredholm integro-differential equation

ME Durmaz, GM Amiraliyev - Mediterranean Journal of Mathematics, 2021 - Springer
In this paper, we deal with a fitted second-order homogeneous (non-hybrid) type difference
scheme for solving the singularly perturbed linear second-order Fredholm integro …

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 …

A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem

SK Sahoo, V Gupta - Computers & Mathematics with Applications, 2023 - Elsevier
The design and analysis of a finite difference method for solving a class of time-fractional
singularly perturbed convection-diffusion problems is the subject of this paper. The time …

[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 …