Numerical analysis of singular perturbation problems

Singular perturbation problems, as exemplified by an initial-boundary value problem, are considered, taking into account the numerical solution of these problems for small epsilon, greater than zero. Problems with the considered characteristics arise in the modeling of convective dominated flow of heat, or the modeling of the diffusion of species, in a moving medium. Equations of a somewhat similar, although more complicated, character are used to study the spread of vorticity in fluid flow. For these reasons, a good insight into the numerical solution of the model problems may lead to improved methods for solving the more complicated problems which occur in nature. Attention is given to boundary and interior layers, loss of stability, and details of numerical analysis.