Mathematical Sciences: A General Approach for the Numerical Solution of DAEs

数学科学：DAE 数值解的通用方法

• 批准号: 9122745
• 负责人: Stephen Campbell
• 金额: $ 13.5万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-15 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9122745&HistoricalAwards=false
• 关键词: Mathematical; Sciences; General; Approach; Numerical

A differential algebraic equation (DAE) is an implicit ordinary differential equation of the form F(y,y,u(t),t)=0 where y(t) is a vector valued function, the Jacobian F y is a singular matrix, and u(t) is a vector valued function of source or control terms. Many problems are most naturally initially modeled as a DAE. They arise, for example, in a variety of control problems in flight control, robotics, chemical process control, and contact or constrained problems in mechanics. In addition, differential algebraic equations occur in the solution of partial differential equations by the method of lines and in many circuit models. DAEs are sometimes also called singular or descriptor systems. The long range goal of the proposed research is for scientists and engineers to be able to work directly with the original implicit model thus reducing design and simulation time as well as facilitating the consideration of more complex problems. Existing numerical codes, while very useful, require special problem structure and do not handle many problems of interest. This project will develop a general numerical method for nonlinear differential algebraic equations. These results will also be of interest when explicit models exist, but the sparsity, nonlinearity, or dependence on parameters of the equations, make the original implicit system preferable to a lower order, but non-sparse, (or difficult to compute local) explicit system.

微分代数方程 (DAE) 是 F(y,y,u(t),t)=0 形式的隐式常微分方程，其中 y(t) 是向量值函数，雅可比 F y 是奇异矩阵，u(t) 是源项或控制项的向量值函数。 许多问题最初最自然地被建模为 DAE。 例如，它们出现在飞行控制、机器人、化学过程控制中的各种控制问题以及机械中的接触或约束问题中。 此外，微分代数方程出现在用直线法求解偏微分方程以及许多电路模型中。 DAE 有时也称为奇异系统或描述符系统。 拟议研究的长期目标是让科学家和工程师能够直接使用原始隐式模型，从而减少设计和模拟时间，并促进考虑更复杂的问题。 现有的数字代码虽然非常有用，但需要特殊的问题结构并且不能处理许多感兴趣的问题。 该项目将开发非线性微分代数方程的通用数值方法。 当存在显式模型时，这些结果也会引起人们的兴趣，但稀疏性、非线性或对方程参数的依赖性使得原始隐式系统优于低阶但非稀疏（或难以计算局部）的显式系统。