Analytical Approaches to Singular Perturbation Problems of Significance in Applications

9703382 O'Malley华盛顿大学建议继续研究项目“奇异摄动问题在应用中的意义的分析方法”，由Robert E. O'Malley, Jr.教授担任首席研究员。本研究发展了求解具有窄边界、激波或快速变化的过渡层区域的常微分方程和偏微分方程非线性边值问题的渐近方法。研究将强调刚性计算和动态亚稳态，通过一贯的混合渐近/数值研究。我们将特别注意到指数渐近的小项，这些项以前很少受到关注，因为我们现在很清楚，所有阶以上的渐近可能具有关键的物理意义。在整个科学和工程中，经常会遇到涉及奇异摄动边值问题的问题。最著名的例子是流体动力边界层。分析和数值技术必须结合起来有效地解决这些重要问题。这项工作基于一种混合方法来解决由应用需求驱动的模型问题的常微分方程和偏微分方程。

9703382 O'Malley The University of Washington proposes that the research project Analytical Approaches to Singular Perturbation Problems of Significance in Applications be continued, with Professor Robert E. O'Malley, Jr. as the Principal Investigator. The research develops asymptotic methods to solve nonlinear boundary value problems for both ordinary and partial differential equations when solutions feature narrow boundary, shock, or transition layer regions of rapid change. The research will emphasize stiff computation and dynamic metastability, through a consistently hybrid asymptotic/numeric investigation. Special notice will be paid to asymptotically exponentially small terms, which have previously received scant attention, since we are now well aware that asymptotics beyond all orders can be of critical physical significance. Throughout science and engineering, problems often occur which involve singularly perturbed boundary value problems. The best known example is fluid dynamical boundary layers. Analytical and numerical techniques must be combined to effectively attack these important problems. This work rests on a hybrid approach to solving both ordinary and partial differential equations for model problems motivated by application needs.