Accurate numerical scheme for singularly perturbed time delayed parabolic differential equations

Abstract

For the numerical solution of the singularly perturbed parabolic convection- difusion equation with large time delays, a novel class of fitted operator finite difference method is constructed using the Mickens-type scheme. Since the perturbation parameter is the source for the simultaneous occurrence of time-consuming and high-speed phenomena in physical systems that depend on present and past history, our study here is to capture the efect of the parameter on the boundary layer. The time derivative is suitably replaced by a Crank-Nicolson-based scheme, followed by the spatial derivative, which is replaced by a non-standard tted operator scheme. First-order error bounds in space and second-order error bounds in time are established to provide numerical results.