Parameter‐uniform numerical methods for singularly perturbed linear transport problems

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