Interval bounds on the solutions of semi-explicit index-one DAEs. Part 2: computation

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• 作者：Joseph K. Scott (1)
  Paul I. Barton (2)
  
• 关键词：65L80 ; 65G20 ; 34A09 ; 34A40 ; 93B03
• 刊名：Numerische Mathematik
• 出版年：2013
• 出版时间：September 2013
• 年：2013
• 卷：125
• 期：1
• 页码：27-60
• 全文大小：657KB
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• 作者单位：Joseph K. Scott (1)
  Paul I. Barton (2)
  
  1. Massachusetts Institute of Technology, 77 Massachusetts Ave 66-363, Cambridge, MA, 02139, USA
  2. Massachusetts Institute of Technology, 77 Massachusetts Ave 66-464, Cambridge, MA, 02139, USA
  

文摘

This article presents two methods for computing interval bounds on the solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). Part 1 presents theoretical developments, while Part 2 discusses implementation and numerical examples. The primary theoretical contributions are (1) an interval inclusion test for existence and uniqueness of a solution, and (2) sufficient conditions, in terms of differential inequalities, for two functions to describe componentwise upper and lower bounds on this solution, point-wise in the independent variable. The first proposed method applies these results sequentially in a two-phase algorithm analogous to validated integration methods for ordinary differential equations (ODEs). The second method unifies these steps to characterize bounds as the solutions of an auxiliary system of DAEs. Efficient implementations of both are described using interval computations and demonstrated on numerical examples.