Second order difference scheme for singularly perturbed boundary turning point problems

A  singularly perturbed convection diffusion  equation with boundary  turning point  is considered in this paper. A higher order method on piecewise uniform Shishkin mesh is suggested to solve this problem. We  prove that this method is of  order O(N^{-۲}(\ln N)^۲). Numerical results are given which validate  the analytical results.

Keywords:

Singular perturbation , boundary turning point , hybrid difference scheme , Shishkin