A modification of the Shishkin discretization mesh for one-dimensional reaction-diffusion problems

In this paper we consider a modification of the Shishkin discretization mesh designed for the numerical solution of one-dimensional singularly perturbed reaction-diffusion problems. The modification consists of a slightly different choice of the transition points between the fine and coarse parts of the mesh. We prove that this change does not affect the order of convergence of the numerical solution obtained by using the central finite-difference scheme. However, due to a better layer-resolving mesh, numerical results show an improvement in the accuracy of the computed solution when compared to the results on the standard Shishkin mesh.