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 Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction‐Diffusion Problem

FW Gelu, GF Duressa - Abstract and applied analysis, 2021 - Wiley Online Library
In this article, a numerical solution is proposed for singularly perturbed delay parabolic
reaction‐diffusion problem with mixed‐type boundary conditions. The problem is discretized …

[PDF][PDF] Uniformly convergent numerical method for singularly perturbed delay parabolic differential equations arising in computational neuroscience

MM Woldaregay, GF Duressa - Kragujevac Journal of mathematics, 2022 - imi.pmf.kg.ac.rs
The motive of this work is to develop ε-uniform numerical method for solving singularly
perturbed parabolic delay differential equation with small delay. To approximate the term …

High‐order schemes and their error analysis for generalized variable coefficients fractional reaction–diffusion equations

A Singh, S Kumar, J Vigo‐Aguiar - Mathematical Methods in …, 2023 - Wiley Online Library
In this manuscript, we develop and analyze two high‐order schemes, CFD g− σ _ g-σ and
PQS g− σ _ g-σ, for generalized variable coefficients fractional reaction–diffusion equations …

[HTML][HTML] Hybrid method for singularly perturbed Robin type parabolic convection–diffusion problems on Shishkin mesh

FW Gelu, GF Duressa - Partial Differential Equations in Applied …, 2023 - Elsevier
This work presents a numerical solution to singularly perturbed Robin-type parabolic
convection–diffusion problems. A hybrid method that combines the central difference …

A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition

N Sharma, A Kaushik - Journal of Applied Mathematics and Computing, 2023 - Springer
A class of singularly perturbed parabolic partial differential equations with a large delay and
an integral boundary condition is studied. The problem's solution features a weak interior …

Accurate numerical scheme for singularly perturbed parabolic delay differential equation

MM Woldaregay, GF Duressa - BMC Research Notes, 2021 - Springer
Objectives Numerical treatment of singularly perturbed parabolic delay differential equation
is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for …

New approach of convergent numerical method for singularly perturbed delay parabolic convection-diffusion problems

ZI Hassen, GF Duressa - Research in Mathematics, 2023 - Taylor & Francis
In this paper, a parameter-uniform convergent numerical scheme is provided for solving
singularly perturbed parabolic convection-diffusion differential equations with a large delay …

An exponentially fitted numerical scheme via domain decomposition for solving singularly perturbed differential equations with large negative shift

AH Ejere, GF Duressa, MM Woldaregay… - Journal of …, 2022 - Wiley Online Library
In this study, we focus on the formulation and analysis of an exponentially fitted numerical
scheme by decomposing the domain into subdomains to solve singularly perturbed …

Parameter robust higher‐order finite difference method for convection‐diffusion problem with time delay

SK Sahoo, V Gupta - Numerical Methods for Partial Differential …, 2023 - Wiley Online Library
This paper deals with the study of a higher‐order numerical approximation for a class of
singularly perturbed convection‐diffusion problems with time delay. The method combines a …