Analytical Approaches to Singular Perturbation Problems of Significance in Applications

具有应用意义的奇异摄动问题的分析方法

• 批准号: 9703382
• 负责人: Robert O'Malley
• 金额: $ 3万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703382&HistoricalAwards=false
• 关键词: Analytical; Approaches; Singular; Perturbation; Problems

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.

9703382 O'Malley华盛顿大学提出研究项目分析方法在应用中的奇异扰动问题中，小罗伯特·E·奥马利教授（Robert E. O'Malley，Jr。）担任首席研究员。 当解决方案具有快速变化的狭窄边界，冲击或过渡层区域时，该研究开发了解决普通微分方程和部分微分方程的非线性边界值问题的渐近方法。 这项研究将通过一贯的混合渐近/数字研究强调僵硬的计算和动态亚竞争性。 特殊通知将涉及以前已受到关注的渐近小术语，因为我们现在非常意识到，除了所有订单以外的渐近学可能具有至关重要的身体意义。 在整个科学和工程中，经常发生问题，涉及奇特的边界价值问题。 最著名的例子是流体动态边界层。 必须合并分析和数值技术，以有效攻击这些重要问题。 这项工作基于一种混合方法，用于解决由应用需求激发的模型问题的普通和部分微分方程。