A domain decomposition method for solving singularly perturbed parabolic reaction‐diffusion problems with time delay

J Singh, S Kumar, M Kumar - Numerical Methods for Partial …, 2018 - Wiley Online Library
We design and analyse a domain decomposition method for solving singularly perturbed
parabolic reaction‐diffusion problems with time delay. Using the asymptotic behavior of the …

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 …

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 …

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] A robust overlap** Schwarz domain decomposition algorithm for time-dependent singularly perturbed reaction–diffusion problems

S Kumar, SCS Rao - Journal of computational and applied mathematics, 2014 - Elsevier
In this work, we consider a singularly perturbed parabolic problem of reaction–diffusion type.
To solve this problem numerically we develop an overlap** Schwarz domain …

A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems

JB Munyakazi, KC Patidar - Computational and applied mathematics, 2013 - Springer
This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We
semidiscretize the problem in time by means of the classical backward Euler method. We …

Fitted computational method for singularly perturbed convection-diffusion equation with time delay

SK Tesfaye, GF Duressa, MM Woldaregay… - Frontiers in Applied …, 2023 - frontiersin.org
A uniformly convergent numerical scheme is proposed to solve a singularly perturbed
convection-diffusion problem with a large time delay. The diffusion term of the problem is …

Parameter-uniform convergence analysis of a domain decomposition method for singularly perturbed parabolic problems with Robin boundary conditions

S Kumar, Aakansha, J Singh, H Ramos - Journal of Applied Mathematics …, 2023 - Springer
We construct and analyze a domain decomposition method to solve a class of singularly
perturbed parabolic problems of reaction-diffusion type having Robin boundary conditions …

Spline-based parameter-uniform scheme for fourth-order singularly perturbed differential equations

S Singh, D Kumar - Journal of Mathematical Chemistry, 2022 - Springer
This paper considers a numerical study for the fourth-order singularly perturbed boundary
value problems. The associated differential equation is converted into a weakly coupled …

Higher order numerical approximations for non-linear time-fractional reaction–diffusion equations exhibiting weak initial singularity

A Singh, S Kumar - Communications in Nonlinear Science and Numerical …, 2024 - Elsevier
In the present study, we introduce a high-order non-polynomial spline method designed for
non-linear time-fractional reaction–diffusion equations with an initial singularity. The method …