Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term

Abstract

A singularly perturbed delay parabolic problem of convection-diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers and weak boundary layers are exhibited due to a large delay in the spatial variable and discontinuity of convection coefficient and source. The problem is discretized by a nonstandard finite difference scheme in the spatial variable and for the time derivative, we used the Crank–Nicolson scheme. To enhance the order of convergence of the spatial variable, the Richardson extrapolation technique is applied. The error analysis of the proposed scheme was carried out and proved that the scheme is uniformly convergent of second order in both spatial and temporal variables. Numerical experiments are performed to verify the theoretical estimates.