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

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 C1C1-norm is established. Numerical results are given to illustrate the theoretical error bounds.