A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling only used within the layers) are shown to be parameter uniformly convergent to the scaled first derivatives of the continuous solution.
@article{arxiv.1708.00682,
title = {Numerical approximations to the scaled first derivatives of a two parameter singularly perturbed problem},
author = {Eugene O'Riordan and Maria Pickett},
journal= {arXiv preprint arXiv:1708.00682},
year = {2017}
}