Interval bounds on the solutions of semi-explicit index-one DAEs. Part 1: analysis
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Author(s)
Scott, Joseph Kirk
Barton, Paul I
Date Issued
March 2013
Journal
Numerische Mathematik
Publisher
Springer Berlin Heidelberg
Citation
Scott, Joseph K., and Paul I. Barton. “Interval Bounds on the Solutions of Semi-Explicit Index-One DAEs. Part 1: Analysis.” Numerische Mathematik 125.1 (2013): 1–25.
Version
Author's final manuscript
Abstract
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. 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.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00211-013-0531-y
