Numerical approximation of solution derivatives in the case of singularly perturbed time dependent reaction-diffusion problems

摘要

Numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a classical finite difference operator on a piecewise-uniform Shishkin mesh. First order convergence of these numerical approximations in an appropriately weighted C-1-norm is established. Numerical results are given to illustrate the theoretical error bounds. (C) 2014 Elsevier B.V. All rights reserved.