Ph.D., University of Maryland at College Park, 1985
Our research interests include singular perturbation problems,
partial differential equations, and asymptotic-induced numerical methods.
Many problems arising from biology, engineering, and physics are dominated by convective processes. These problems are characterized by a class of ordinary or partial differential equations in which a small positive parameter multiplies the highest derivative term. In such problems the solution changes abruptly in a small region, either near the boundary of the domain or along a curve internal to the domain, whose width tends to zero as the parameter tends to zero. Typically, such solutions are said to possess a boundary or internal layer behavior. The structure of the layer in these problems is described by finding its governing equations subject to auxiliary conditions by virtue of singular perturbation techniques, and this structure is used in designing accurate, and stable numerical methods of computing the solutions.
Current research problems include