A deep learning feed-forward neural network framework for the solutions to singularly perturbed delay differential equations

SM Mallikarjunaiah - Applied Soft Computing, 2023 - Elsevier
In this paper, we explore a deep learning feedforward artificial neural network (ANN)
framework as a numerical tool for approximating the solutions to singularly perturbed delay …

Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

A Das, S Natesan - Applied Mathematics and Computation, 2015 - Elsevier
This article studies the numerical solution of singularly perturbed delay parabolic convection–
diffusion initial-boundary-value problems. Since the solution of these problems exhibit …

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction–diffusion boundary-value problems

P Das, S Natesan - Applied mathematics and computation, 2014 - Elsevier
In this article, we study the problem of determining an appropriate grading of meshes for a
system of coupled singularly perturbed reaction–diffusion problems having diffusion …

ε-Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations

S Gowrisankar, S Natesan - International Journal of Computer …, 2017 - Taylor & Francis
This paper studies the numerical solutions of singularly perturbed parabolic convection–
diffusion problems with a delay in time. We divide the domain using a piecewise uniform …

A second order numerical method for singularly perturbed delay parabolic partial differential equation

L Govindarao, J Mohapatra - Engineering Computations, 2019 - emerald.com
Purpose The purpose of this paper is to provide a robust second-order numerical scheme for
singularly perturbed delay parabolic convection–diffusion initial boundary value problem …

An initial value technique for singularly perturbed convection–diffusion problems with a negative shift

V Subburayan, N Ramanujam - Journal of Optimization Theory and …, 2013 - Springer
In this paper, a numerical method named as Initial Value Technique (IVT) is suggested to
solve the singularly perturbed boundary value problem for the second order ordinary …

[HTML][HTML] Asymptotic initial value technique for singularly perturbed convection–diffusion delay problems with boundary and weak interior layers

V Subburayan, N Ramanujam - Applied Mathematics Letters, 2012 - Elsevier
In this paper a numerical method named as Asymptotic Initial Value Technique (AIVT) is
suggested to solve the singularly perturbed boundary value problem for the second order …

Uniformly convergent numerical method for singularly perturbed differential‐difference equation using grid equidistribution

J Mohapatra, S Natesan - International Journal for Numerical …, 2011 - Wiley Online Library
In this paper, a class of singularly perturbed differential‐difference equations with small
delay and shift terms is considered. A numerical method comprising of upwind finite …

[HTML][HTML] An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift

PA Selvi, N Ramanujam - Journal of Computational and Applied …, 2016 - Elsevier
In this paper, a numerical method based on an iterative scheme is proposed for a singularly
perturbed delay differential equation of reaction–diffusion type. In this method the solution of …

Fitted finite difference method for third order singularly perturbed delay differential equations of convection diffusion type

R Mahendran, V Subburayan - International journal of …, 2019 - World Scientific
In this paper, a fitted finite difference method on Shishkin mesh is suggested to solve a class
of third order singularly perturbed boundary value problems for ordinary delay differential …