A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems

K Kumar, PC Podila, P Das… - Mathematical Methods in …, 2021 - Wiley Online Library
In this work, we consider a graded mesh refinement algorithm for solving time‐delayed
parabolic partial differential equations with a small diffusion parameter. The presence of this …

Novel Numerical Scheme for Singularly Perturbed Time Delay Convection‐Diffusion Equation

MM Woldaregay, WT Aniley… - … in Mathematical Physics, 2021 - Wiley Online Library
This paper deals with numerical treatment of singularly perturbed parabolic differential
equations having large time delay. The highest order derivative term in the equation is …

[HTML][HTML] A robust fitted numerical scheme for singularly perturbed parabolic reaction–diffusion problems with a general time delay

NT Negero - Results in Physics, 2023 - Elsevier
The present paper deals with the class of time-delayed, singularly perturbed parabolic
reaction–diffusion problems. In the x− t plane, parabolic boundary layers appear on the two …

A parameter‐uniform scheme for singularly perturbed partial differential equations with a time lag

D Kumar, P Kumari - Numerical Methods for Partial Differential …, 2020 - Wiley Online Library
A numerical scheme for a class of singularly perturbed delay parabolic partial differential
equations which has wide applications in the various branches of science and engineering …

Parameter uniform hybrid numerical method for time-dependent singularly perturbed parabolic differential equations with large delay

ZI Hassen, GF Duressa - Applied Mathematics in Science and …, 2024 - Taylor & Francis
In this study, to solve the singularly perturbed delay convection–diffusion–reaction problem,
we proposed a hybrid numerical scheme that converges uniformly. Parabolic right boundary …

A uniformly convergent numerical scheme for solving singularly perturbed differential equations with large spatial delay

AH Ejere, GF Duressa, MM Woldaregay, TG Dinka - SN Applied Sciences, 2022 - Springer
In this study, a parameter-uniform numerical scheme is built and analyzed to treat a
singularly perturbed parabolic differential equation involving large spatial delay. The …

A stable finite difference scheme and error estimates for parabolic singularly perturbed PDEs with shift parameters

K Kumar, PP Chakravarthy, H Ramos… - Journal of Computational …, 2022 - Elsevier
This article presents a stable finite difference approach for the numerical approximation of
singularly perturbed differential-difference equations (SPDDEs). The proposed scheme is …

Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline

PMM Kumar, ASV Ravi Kanth - Computational and Applied Mathematics, 2020 - Springer
This article contributes a numerical technique for a class of singularly perturbed time
delayed parabolic partial differential equation. A priori results of maximum principle, stability …

[HTML][HTML] An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

PP Chakravarthy, SD Kumar, RN Rao - Ain Shams Engineering Journal, 2017 - Elsevier
This paper deals with singularly perturbed boundary value problem for a linear second order
delay differential equation. It is known that the classical numerical methods are not …

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 …