  Pointwise accurate numerical methods are constructed and analysed for three
classes of singularly perturbed first order transport problems. The methods
involve piecewise-uniform Shishkin meshes and the numerical approximations are
shown to be parameter-uniformly convergent in the maximum norm. A transport
problem from the modelling of fluid-particle interaction is formulated and used
as a test problem for these numerical methods. Numerical results are presented
to illustrate the performance of the numerical methods and to confirm the
theoretical error bounds established in the paper.
