Numerical Analysis of Singular Perturbations and Convection-Diffusion Equations

奇异扰动和对流扩散方程的数值分析

• 批准号: 8806733
• 负责人: Eugene Gartland
• 金额: --
• 依托单位: Kent State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8806733&HistoricalAwards=false
• 关键词: Numerical; Analysis; Singular; Perturbations; Convection

This project is concerned with the numerical analysis of singularly perturbed ordinary and partial differential equations. Standard numerical approaches have difficulty in such situations. The main objective of this project is to develop tools for the construction and analysis of high order finite-difference discretizations for these problems. The methods employed will consist of a combination of classical and modern notions of consistency, stability, and regularity. The development of the discretization schemes will use a general finite-difference framework and will take place in an environment of realistic numerical experimentation and rigorous mathematical analysis.

本项目涉及的数值分析 奇摄动常微分方程和偏微分方程。 标准的数值方法在这种情况下有困难。 该项目的主要目标是开发工具， 高阶有限差分格式的构造与分析 这些问题的离散化。 所采用的方法将 由古典和现代观念的结合组成， 一致性、稳定性和规律性。 的发展 离散方案将使用一般的有限差分 框架，并将在现实的环境中进行 数值实验和严格的数学分析。