A Fourier Approach to the Analysis and Design of Numerical Methods for Differencial Equations

微分方程数值方法分析与设计的傅里叶方法

• 批准号: 9009323
• 负责人: Chung-Chieh Jay Kuo
• 金额: $ 6万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009323&HistoricalAwards=false
• 关键词: Fourier; Approach; Analysis; Design; Numerical

The numerical solution of ordinary and partial differential equations (ODEs and PDEs) provides an important class of large scale scientific computing problems. Fourier analysis has been used by applied mathematicians as a simple and effective tool to analyze the numerical properties of approximation schemes and solution methods for ODEs and PDEs. This includes three main objectives: (1) exploiting Fourier tools used in the areas of digital filtering and digital control for solving ODEs and elliptic PDEs, (2) analyzing numerical ODE and elliptic PDE algorithms with Fourier techniques so that they can be understood by electrical engineers in a more familiar setting, and (3) development of new parallel algorithms and study of their performnce on parallel algorithms and study of their performance on parallel computers such as the Connection Machine CM/2 and Alliant FX/80.

常微分方程组和偏微分方程组的数值解是一类重要的大规模科学计算问题。傅立叶分析已被应用数学家作为一种简单而有效的工具来分析常微分方程组和偏微分方程组的逼近格式和求解方法的数值性质。这包括三个主要目标：(1)利用在数字滤波和数字控制领域中使用的傅立叶工具来求解常微分方程组和椭圆型偏微分方程组，(2)利用傅立叶技术分析数值常微分方程组和椭圆型偏微分方程组算法，以便电气工程师能够在更熟悉的环境中理解它们，(3)开发新的并行算法，研究它们在并行算法上的性能，并研究它们在连接机CM/2和Aliant FX/80等并行机上的性能。