A uniformly convergent exponential spline difference scheme for singularly perturbed reaction-diffusion problems

Abstract

We consider a Dirichlet boundary value problem for singularly perturbed reaction-diffusion equation. The problem is discretized using an exponential spline difference scheme derived on the basis of splines in tension. The fitted mesh technique is employed to generate piecewise-uniform Shishkin type mesh, condensed in the neighborhood of the boundary layers. The convergence analysis is given and the method is shown to have second order e-uniform convergence on piecewise-uniform Shishkin type mesh. Numerical experiments are conducted to demonstrate the theoretical results.