Mathematical Sciences: Analytical Approaches to Singular Perturbation Problems of Significance in Application

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This project concerns the asymptotic solution of nonlinear boundary value problems whose solutions involve boundary and interior layer regions of rapid change. Extensive numerical computation must be carried out to solve these problems for specific values. Also, involved in the solution is symbolic computation for both regular perturbation problems and for carrying out Poincare-Lindstedt type procedures. Symbolic computation promises new techniques and methods for these problems. This project is in the general area of applied mathematics and, more specifically, in the area of singular perturbations. Of special note in this project will be the use of symbolic computation for boundary layer and shock problems. This research has wide applications to engineering.