Mathematical Sciences: Analytical and Numerical Approaches to Singular Perturbation Problems of Significance in Applications

数学科学：具有应用意义的奇异摄动问题的分析和数值方法

• 批准号: 8805626
• 负责人: Robert O'Malley
• 金额: $ 3.96万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-08-01 至 1990-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805626&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Numerical; Approaches

This research will study the asymptotic solution of nonlinear initial and boundary value problems involving systems of differential equations. A characteristic of the solutions of these equations is that they exhibit rapid changes within thin regions. Consequently, the asymptotic methods are able to make use of the presence of multiple scales. Of particular interest in this research are problems involving boundary and interior layers. The work will be motivated by physical applications including models which simulate the operation of semiconductor devices. Problems will be attacked using a combined analytical and numerical approach.

本研究将研究涉及微分方程组的非线性初边值问题的渐近解。这些方程的解的一个特点是它们在薄区域内表现出快速的变化。因此，渐近方法能够利用多个尺度的存在。在这项研究中特别感兴趣的是涉及边界层和内层的问题。这项工作将受到物理应用的推动，包括模拟半导体器件操作的模型。将使用分析和数值相结合的方法来解决问题。