Analytical Approaches to Singular Perturbation Problems of Significance in Applications

9703382 O‘Malley华盛顿大学建议继续与小Robert E.O’Malley教授合作，研究应用中具有重要意义的奇异摄动问题的分析方法。作为首席调查员。当解具有较窄的边界、激波或快速变化的过渡层区域时，该研究发展了求解常微分方程组和偏微分方程组的非线性边值问题的渐近方法。这项研究将通过一贯的渐近/数值混合调查，强调刚性计算和动态亚稳性。我们将特别注意渐近指数的小项，因为我们现在很清楚，超越所有阶数的渐近可能具有关键的物理意义，以前很少注意到这一点。在整个科学和工程中，经常会出现涉及奇摄动边值问题的问题。最著名的例子是流体动力边界层。必须将分析和数值技术结合起来，才能有效地解决这些重要问题。这项工作依赖于一种混合方法来求解模型问题的常微分方程组和偏微分方程组，以满足应用需求。

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.