A spline difference scheme on a piecewise equidistant grid

Abstract

We consider singularly perturbed boundary value problems of reaction-diffusion type and their discretization via quadratic spline difference schemes on a piecewise equidistant mesh of the Shishkin type. On such a mesh we prove that a solution to the discretisation is almost second order accurate in the discrete maximum norm, uniformly in the perturbation parameter. Numerical results are presented, which verify this rate of convergence.