Numerical algorithms and software for high-index differential-algebraic equations

高指数微分代数方程的数值算法和软件

• 批准号: 227816-2009
• 负责人: Nedialkov, Nedialko
• 金额: $ 1.09万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=524114
• 关键词: Numerical; algorithms; software; index; differential

Many problems in engineering and science are modeled with systems containing both differential and algebraic equations, also called differential-algebraic equations (DAEs). Systems of DAEs arise for example in robotics, circuit simulation, optimal control, and multi-body dynamics. A DAE is characterized by its index, which measures how difficult it is solve the DAE numerically. The higher the index, the more difficult the solution process is. Standard numerical methods for DAEs usually handle only one form or class of DAEs and are typically restricted to at most index-3 problems.

工程和科学中的许多问题都是用包含微分方程和代数方程的系统建模的，也称为微分代数方程（DAEs）。DAEs系统出现在机器人、电路仿真、最优控制和多体动力学等领域。DAE的特征是它的指数，它衡量了用数值方法求解DAE的难易程度。指数越高，说明求解过程越困难。DAEs的标准数值方法通常只处理DAEs的一种形式或一类，并且通常限于最多index-3问题。