We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markov-modulated queues. We employ singular perturbation methods to study th...

A singularly perturbed time-dependent convection-diffusion problem is examined on non-rectangular domains. The nature of the boundary and interior layers that arise depends on the geometry of the domains. For problems with different types of layers, various numerical methods are constructed to resolve the layers in the solutions and the numerical solutions are shown to converge independently of...

A class of singularly perturbed quasilinear differential equations with discontinuous data is examined. In general, interior layers will appear in the solutions of problems from this class. A numerical method is constructed for this problem class, which involves an appropriate piecewise-uniform mesh. The method is shown to be a parameter-uniform numerical method with respect to the singular per...

Singularly perturbed problems of convection-diiusion type are dif-cult to solve using standard numerical methods. This shows that it is desirable to construct robust methods that converge uniformly in the singular perturbation parameter. In this paper we derive new conditions that schemes of this type must satisfy, with particular reference to the case of parabolic layers.

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markovmodulated queues. We employ singular perturbation methods to study the...