Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations

Abstract

A study is made of a class of boundary-value problems for linear second-order differential-difference equations in which the highest-order derivative is multiplied by a small parameter. Consideration of the exact solution of simple model equations provides insight into the appropriate use of singular perturbation techniques for more general problems. The resulting analysis leads to several novel features which are not present in problems without differences.