•  
  •  
 

Abstract

This article deals with solving a system of n time-dependent singularly perturbed problems with spatial delay and robin initial conditions. Each equation’s leading term is multiplied by a distinct small positive parameter, inducing overlapping initial layers. Due to presence of these parameters and delay terms, intricate layers occur at interior regions of the domain. To capture the behavior of these layers the solution is decomposed into two components and layer functions are also formulated. The formulation of the layer resolving numerical scheme involves temporal and spatial discretization on uniform and piecewise uniform Shishkin meshes respectively. The proposed framework is found to possess nearly first-order parameter uniform convergence in the spatial axis and also first-order convergence in the temporal axis. At last, to bolster the theoretical result, a numerical scheme is constructed for an example problem by showing better convergence rate and error constant to prove efficacy of the proposed scheme.

Download

Share

COinS