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 …

Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations

V Gupta, M Kumar, S Kumar - Numerical Methods for Partial …, 2018 - Wiley Online Library
In this article, we develop a higher order numerical approximation for time dependent
singularly perturbed differential‐difference convection‐diffusion equations. A priori bounds …

[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 …

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 …

[HTML][HTML] A variable stepsize hybrid block optimized technique for integrating a class of singularly perturbed parabolic problems

MA Rufai, H Ramos, B Carpentieri - Results in Applied Mathematics, 2024 - Elsevier
This paper presents and successfully applies an optimized hybrid block technique using a
variable stepsize implementation to integrate a type of singularly perturbed parabolic …

[HTML][HTML] Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation

N Senu, KC Lee, A Ahmadian, SNI Ibrahim - Alexandria Engineering …, 2022 - Elsevier
Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order
(TDRKT3 (5)) is developed and proposed for solving a special type of third-order delay …

Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions

S Kumar, H Ramos - Applied Mathematics and Computation, 2021 - Elsevier
In this work we develop a parameter-uniform numerical method on equidistributed meshes
for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin …

High‐order convergent methods for singularly perturbed quasilinear problems with integral boundary conditions

S Kumar, S Kumar, Sumit - Mathematical Methods in the …, 2024 - Wiley Online Library
In this work, we develop a numerical scheme for a class of singularly perturbed quasilinear
problems with integral boundary conditions. The quasilinear equation is discretized using a …

Analysis of a nonlinear singularly perturbed Volterra integro-differential equation

S Kumar, J Vigo-Aguiar - Journal of Computational and Applied …, 2022 - Elsevier
We consider a nonlinear singularly perturbed Volterra integro-differential equation. The
problem is discretized by an implicit finite difference scheme on an arbitrary non-uniform …

A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems

S Kumar, M Kumar - Numerical Algorithms, 2017 - Springer
In this work, we propose a hybrid difference scheme for solving parameterized singularly
perturbed delay differential problems. A unified error analysis framework for the proposed …