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The paper is published in:
P.J. Laurent, A. Le Mehaute and L.L. Schumaker (eds.):
Curves and Surfaces in Geometric Design,
Wellesley: A K Peters, 1994, pp. 918.
 MSC:
 65L05 Initial value problems
 28B20 Setvalued set functions and measures; integration of setvalued functions; measurable selections, See Also {26E25, 54C60, 54C65, 90A14}
 34A60 Equations with multivalued righthand sides, See Also
 Keywords:
 order of convergence; Hausdorff distance; Aumann's integral; extrapolation method; Romberg's method; reachable sets; linear differential inclusions; linear control problems
 Abstract:

Order of convergence results with respect to Hausdorff distance are summarized for the numerical approximation of
Aumann's integral by an extrapolation method which is the setvalued analogue of Romberg's method. This method is
applied to the discrete approximation of reachable sets of linear differential inclusions. For a broad class of linear control
problems, it yields at least second order of convergence, for problems with additional implicit smoothness properties even
higher order of convergence.
 Table of Contents:

1. Introduction
2. SetValued Integration
3. Approximation of Reachable Sets
4. Concluding Remarks
©
Robert Baier
Last modified: Thu May 28 14:57:20 MDT 1998