On Nonlinear Singularly Perturbed Initial Value Problems

The study of singularly perturbed initial value problems for nonlinear systems of ordinary differential equations parallels the analysis underlying the development of numerical algorithms for obtaining solutions to systems of stiff differential equations. This paper seeks to emphasize the advantages of combining these two substantial research efforts. It develops insight and intuition based on a sequence of solvable model problems, and it relates a variety of literature scattered throughout asymptotic and numerical analyses, stability and control theory and specific topics in applied mathematical modeling.