A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems

S Priyadarshana, J Mohapatra, SR Pattanaik - Applied Numerical …, 2023 - Elsevier
The objective of this work is to provide an efficient and higher-order numerical scheme for
the solution of a singularly perturbed 2D time-delayed parabolic convection-diffusion …

Uniformly convergent computational method for singularly perturbed time delayed parabolic differential-difference equations

J Mohapatra, S Priyadarshana… - Engineering …, 2023 - emerald.com
Purpose The purpose of this work is to introduce an efficient, global second-order accurate
and parameter-uniform numerical approximation for singularly perturbed parabolic …

An improved time accurate numerical estimation for singularly perturbed semilinear parabolic differential equations with small space shifts and a large time lag

S Priyadarshana, J Mohapatra, SR Pattanaik - … and Computers in …, 2023 - Elsevier
The objective of this work is to provide a robust numerical scheme for solving a singularly
perturbed semilinear parabolic differential–difference equation having both time delay along …

[HTML][HTML] A numerical approach for a two-parameter singularly perturbed weakly-coupled system of 2-D elliptic convection–reaction–diffusion PDEs

C Clavero, R Shiromani, V Shanthi - Journal of Computational and Applied …, 2024 - Elsevier
In this work, we consider the numerical approximation of a two dimensional elliptic singularly
perturbed weakly-coupled system of convection–reaction–diffusion type, which has two …

An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag

S Priyadarshana, J Mohapatra - Indian Journal of Pure and Applied …, 2023 - Springer
The objective of this work is to provide an efficient numerical scheme for solving singularly
perturbed parabolic convection-diffusion problems with a large time lag having Robin-type …

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 …

Weighted variable based numerical scheme for time-lagged semilinear parabolic problems including small parameter

S Priyadarshana, J Mohapatra - Journal of Applied Mathematics and …, 2023 - Springer
A higher-order robust numerical algorithm is proposed for singularly perturbed semilinear
parabolic partial differential equations having time lag. After dealing the semilinearity with …

Numerical integration method for two-parameter singularly perturbed time delay parabolic problem

SL Cheru, GF Duressa, TB Mekonnen - Frontiers in Applied …, 2024 - frontiersin.org
This study presents an (ε, μ)− uniform numerical method for a two-parameter singularly
perturbed time-delayed parabolic problems. The proposed approach is based on a fitted …

An efficient computational technique for time dependent semilinear parabolic problems involving two small parameters

S Priyadarshana, J Mohapatra - Journal of Applied Mathematics and …, 2023 - Springer
The present work discusses a robust numerical scheme for singularly perturbed semilinear
parabolic problems with two small parameters. Unlike many works in the literature, the …

Difference potentials method for the nonlinear convection-diffusion equation with interfaces

MT Tameh, F Shakeri - Applied Numerical Mathematics, 2024 - Elsevier
In this paper, the difference potentials method-based ADI finite difference scheme is
proposed for numerical solutions of two-dimensional nonlinear convection–diffusion …