Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time

S Saini, P Das, S Kumar - Applied Numerical Mathematics, 2024 - Elsevier
In this paper, we address a class of boundary layer originated singularly perturbed parabolic
reaction-diffusion problems with Robin boundary conditions having large time delay; for the …

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 …

Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers

S Saini, P Das, S Kumar - Revista de la Real Academia de Ciencias …, 2023 - Springer
In this article, we consider the computational cost reduction of approximating a coupled
system of time variant multiscale parameterized problems with mixed type conditions, in …

Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis

P Das, S Rana - Mathematical Methods in the Applied Sciences, 2021 - Wiley Online Library
In this research, we study a weakly singular Volterra integro differential equation with
Caputo‐type fractional derivative. First, we derive a sufficient condition for the existence and …

A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic BB‐spline

R Choudhary, S Singh, P Das… - Mathematical Methods in …, 2024 - Wiley Online Library
This article deals with designing and analyzing a higher order stable numerical analysis for
the time‐fractional Kuramoto–Sivashinsky (K‐S) equation, which is a fourth‐order non …

Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations

A Panda, S Santra, J Mohapatra - Journal of Applied Mathematics and …, 2022 - Springer
This article deals with two different methods to solve a time fractional partial integro-
differential equation. The fractional derivatives are defined here in Caputo sense. The model …

Parameter uniform optimal order numerical approximations for time-delayed parabolic convection diffusion problems involving two small parameters

S Priyadarshana, J Mohapatra, SR Pattanaik - Computational and Applied …, 2022 - Springer
The purpose of this work is to provide robust numerical scheme for singularly perturbed time
delay (large) convection-reaction-diffusion problem with two small parameters. The work …

Robust numerical method for singularly perturbed semilinear parabolic differential difference equations

MJ Kabeto, GF Duressa - Mathematics and Computers in Simulation, 2021 - Elsevier
This paper deals with the robust numerical method for solving the singularly perturbed
semilinear partial differential equation with the spatial delay. The quadratically convergent …

A uniformly convergent analysis for multiple scale parabolic singularly perturbed convection-diffusion coupled systems: Optimal accuracy with less computational time

S Kumar, P Das - Applied Numerical Mathematics, 2025 - Elsevier
This study addresses time-dependent multiple-scale reaction-convection-diffusion initial
boundary value systems characterized by strong coupling in the reaction matrix and weak …

Impact of mixed boundary conditions and nonsmooth data on layer‐originated nonpremixed combustion problems: Higher‐order convergence analysis

S Kumar, P Das - Studies in Applied Mathematics, 2024 - Wiley Online Library
This work explores the theoretical and computational impacts of mixed‐type flux conditions
and nonsmooth data on boundary/interior layer‐originated singularly perturbed semilinear …