Performance of Richardson extrapolation on some numerical methods for a singularly perturbed turning point problem whose solution has boundary layers (Q2877775)

The authors apply the Richardson extrapolation technique to some numerical schemes for solving singularly perturbed turning point problems. Generally, the solutions of singularly perturbed turning point problems exhibit either exponential boundary layers or interior layers. In this paper, the authors consider the first case, to solve these problems numerically; exponentially fitted difference schemes (also known as fitted operator methods) and finite difference schemes on piecewise-uniform Shishkin meshes are available in the literature. Also, the Richardson extrapolation technique is well-known, the post-processing technique exists in the literature to improve the order of accuracy. Here, the authors combine these two techniques to improve the accuracy of the numerical solution of singularly perturbed turning point problems. But there is no improvement in the final results. After extrapolation also, the convergence rate still remain first-order only. The authors do not provide any mathematical reasons for not achieving the second-order convergence rate. The numerical results remain almost the same both before and after the Richardson extrapolation, which requires calculating the solution twice on two different grids (computationally expensive).