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

本课题研究非线性方程组的渐近解 边值问题，其解涉及边界和 快速变化的内层区域。 广泛的数值 必须进行计算来解决这些问题， 具体的价值观。 此外，参与解决方案具有象征意义 计算正则摄动问题和携带 庞加莱-林斯泰德式的手术 符号计算 为解决这些问题提供了新的技术和方法。 该项目属于应用数学的一般领域 更具体地说，是在奇异摄动领域。 的 在这个项目中特别注意将使用象征性的 边界层和激波问题的计算。 本研究 在工程上有着广泛的应用。

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.