Construction and Implementation of Efficient Numerical Methods for Ordinary Differential Equations

常微分方程高效数值方法的构建与实现

• 批准号: 0509597
• 负责人: Zdzislaw Jackiewicz
• 金额: $ 9.1万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0509597&HistoricalAwards=false
• 关键词: Construction; Implementation; Efficient; Numerical; Methods

Many problems in science and engineering are modelled by large systems of differential equations. It is the purpose of the research described in this proposal to design and implement accurate, efficient, reliable, and robust methods for the numerical simulations of such systems. These methods should be capable of exploiting special structure often present in such systems to increase the computational efficiency. Examples of such systems with special structure include many problems in computational fluid dynamics, molecular biology, quantum mechanics, and heat transfer, and their numerical solution requires new more powerful numerical techniques than the classical methods. The novel techniques which will be investigated in this proposal are based on the recent theory of general linear methods and on exponential integrators which treat differently specific parts of the differential systems. Some of the proposed schemes are appropriate for implementation in a parallel computing environment.

科学和工程中的许多问题都是由大型的微分方程组来模拟的。 这是本提案中所描述的研究的目的，设计和实施准确，高效，可靠，鲁棒的方法，这种系统的数值模拟。 这些方法应该能够利用这种系统中经常出现的特殊结构来提高计算效率。 这类具有特殊结构的系统的例子包括计算流体力学、分子生物学、量子力学和传热学中的许多问题，它们的数值求解需要比经典方法更强大的新的数值技术。 新的技术，这将是调查在这个建议是基于最近的理论一般线性方法和指数积分器，不同的处理特定部分的微分系统。 所提出的一些方案是适合在并行计算环境中实施。