Publication

Abstract : This paper presents a numerical solution for a time delay parabolic problem (reaction-diffusion) containing a small parameter. The numerical method combines the implicit Crank–Nicolson scheme for the time derivative on the uniform mesh and the central difference scheme for the spatial derivative on the Shishkin-type meshes. It is shown to be second-order uniformly convergent in time and space. Then Richardson extrapolation technique is applied to enhance the accuracy from second-order to fourth-order. The error analysis is carried out, and the method is proved to be uniformly convergent. These two methods are applied to two test examples in support of the theoretical results.