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 …

Collocation method using artificial viscosity for time dependent singularly perturbed differential–difference equations

IT Daba, GF Duressa - Mathematics and Computers in Simulation, 2022 - Elsevier
A parameter uniform numerical method is presented for solving singularly perturbed time-
dependent differential–difference equations with small shifts. To approximate the terms with …

A novel algorithm for singularly perturbed parabolic differential-difference equations

IT Daba, GF Duressa - Research in Mathematics, 2022 - Taylor & Francis
In this study, numerical treatment of singularly perturbed parabolic partial differential-
difference equations with small mixed shifts arising in computational neuroscience is …

[HTML][HTML] Layer resolving numerical scheme for singularly perturbed parabolic convection-diffusion problem with an interior layer

GR Kusi, AH Habte, TA Bullo - MethodsX, 2023 - Elsevier
Singularly perturbed parabolic convection-diffusion problem with interior layer is a type of
singularly perturbed boundary value problems which have sign change properties in the …

Uniformly convergent numerical scheme for singularly perturbed parabolic pdes with shift parameters

MM Woldaregay, GF Duressa - Mathematical Problems in …, 2021 - Wiley Online Library
In this article, singularly perturbed parabolic differential difference equations are considered.
The solution of the equations exhibits a boundary layer on the right side of the spatial …

Fitted tension spline method for singularly perturbed time delay reaction diffusion problems

EA Megiso, MM Woldaregay… - … Problems in Engineering, 2022 - Wiley Online Library
A uniformly convergent numerical method is presented for solving singularly perturbed time
delay reaction‐diffusion problems. Properties of the continuous solution are discussed. The …

A hybrid numerical scheme for singularly perturbed parabolic differential‐difference equations arising in the modeling of neuronal variability

I Takele Daba, G File Duressa - … and Mathematical Methods, 2021 - Wiley Online Library
This study aims at constructing a robust numerical scheme for solving singularly perturbed
parabolic delay differential equations arising in the modeling of neuronal variability. Taylor's …

Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers

TA Bullo, GR Kusi - Reaction Kinetics, Mechanisms and Catalysis, 2024 - Springer
In this paper, fitted mesh numerical scheme is presented for solving singularly perturbed
parabolic convection–diffusion problem exhibiting twin boundary layers. To approximate the …

Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts

T Prathap, RN Rao - Journal of Applied Mathematics and Computing, 2023 - Springer
In this paper, exponentially fitted finite difference methods are presented for singularly
perturbed one-dimensional parabolic partial differential equation with mixed shifts in the …

Second-order robust finite difference method for singularly perturbed Burgers' equation

MJ Kabeto, GF Duressa - Heliyon, 2022 - cell.com
In this paper, a second-order robust method for solving singularly perturbed Burgers'
equation were presented. To find the numerical approximation, we apply the …