Paper's Title:

Robust Layer Resolving Scheme for a System of Two Singularly Perturbed Time-Dependent Delay Initial Value Problems with Robin Initial Conditions

Author(s):

¹K. Ramiya Bharathi, ²G. E. Chatzarakis, ²S. L. Panetsos, and ¹M. Joseph Paramasivam

¹PG & Research Department of Mathematics,
Bishop Heber College (Affiliated to Bharathidasan University),
Tiruchirappalli - 620 017, Tamil Nadu,
India.
E-mail: ramiyabharathik28@gmail.com, paramasivam.ma@bhc.edu.i 

²Department of Electrical and Electronic Engineering Educators,
School of Pedagogical \& Technological Education (ASPETE),
Marousi, 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

This paper aimed at proving first order convergence for system of two singularly perturbed time-dependent initial value problems with delay in spatial variable and robin initial conditions. A Classical layer resolving finite difference scheme is developed by implementing uniform mesh for time discretization; Shishkin-mesh, a piecewise uniform mesh for spatial discretization. Shishkin-mesh is constructed is such way it captures the intricacies behavior of the layers. The interior layer is induced by the presence of a delay term in the space term. Error estimate is carried out to prove first order convergence with the help of maximum principle, stability analysis, solution bounds and sharper estimates of the singular components of the solutions. Finally, the numerical illustration is computed for the problem to bolster the scheme.

Paper's Title:

Linear System of Singularly Perturbed Initial Value Problems with Robin Initial Conditions

Author(s):

S. Dinesh, G. E. Chatzarakis, S. L. Panetsos and S. Sivamani

Department of Mathematics,
Saranathan College of Engineering,
Tiruchirappalli-620012,
Tamil Nadu,
India.

Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.

E-mail: geaxatz@otenet.gr, dineshselvaraj24@gmail.com,
spanetsos@aspete.gr, winmayi2012@gmail.com

Abstract:

On the interval (0,1], this paper considers an initial value problem for a system of n singularly perturbed differential equations with Robin initial conditions. On a piecewise uniform Shishkin mesh, a computational approach based on a classical finite difference scheme is proposed. This approach is shown to be first-order convergent in the maximum norm uniformly in the perturbation parameters. The theory is illustrated by a numerical example.

Search and serve lasted 1 second(s).