Classical Layer Resolving Scheme for a System of Two Singularly Perturbed Time-Dependent Problems with Discontinuous Source Terms and Spatial Delay

In this paper we formulate a Classical layer resolving finite difference scheme to solve a system of two singularly perturbed time-dependent problems with discontinuity occurs at (y; t) in the source terms and Robin initial conditions. The delay term occurs in the spatial variable and leading term of spatial derivative of each equation is multiplied by a distinct small positive perturbation parameter, inducing layer behaviors in the solution domain. The formulation of finite difference scheme involves discretization of temporal and spatial axis by uniform and piecewise uniform meshes respectively. Due to presence of perturbation parameters, discontinuous source terms and delay terms, initial and interior layers occur in the solution domain. In order to capture the abrupt change occurs due to the behavior of these layers, the solution is further decomposed into two components. Layer functions are also formulated in accordance with layer behavior. At last, to bolster the numerical scheme, an example problem is computed to prove efficacy of our scheme.