Richardson extrapolation for a singularly perturbed turning point problem with exponential boundary layers

We consider an interior turning point problem with two exponential boundary layers. Its discretisation on a piecewise-uniform Shishkin mesh yields a scheme which is uniformly convergent (measured in the discrete maximum norm) of almost order one. Richardson extrapolation improves the accuracy to O(N−2ln2N)O(N−2ln2N). Both can be proved under the assumption ε≤CN−1ε≤CN−1.