Sp Semi-Linear Parabolic Spatial Des Using Robust Numerical Method

Abstract

In this research, a resilient numerical approach for a coupled system of singly perturbed parabolic delay partial differential equations is designed and analyses. On the regular and layer components of the solution and their derivatives, design a priori bounds are derived. Shishkin and generalized Shishkin type appropriate layer adaptive meshes are defined in the spatial direction based on these a priori constraints. The problem is then discretized using the central difference scheme on layer-adapted Shishkin and generalized Shishkin type meshes in the spatial direction and an implicit Euler scheme on a uniform mesh in the temporal direction. A numerical approach to the issue is proposed, taking into account both generalized Shishkin meshes and relevant layer adapted Shishkin meshes.