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The paper is published in:
ZAMM 74 (1994), No. 6, T555557.
 MSC:
 93B03 Attainable sets
 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
 65L05 Initial value problems
 65L06 Multistep, RungeKutta and extrapolation methods
 Keywords:
 extrapolation methods; setvalued integrals; linear differential inclusions
 Abstract:

The following linear differential inclusion is considered:
where
,
A(.) is an integrable n x nmatrix
function and U(.) is a measurable and integrably bounded
setvalued mapping with nonempty compact images.
The problem is to
approximate the reachable set (the set of all possible endpoints
y(b)) of all absolutely continuous functions
,
satisfying for almost every t the relation above.
An approximation method of order 2j+ 2 is formulated under suitable
assumptions. A numerical example is presented.
[ Review by M.I.Krastanov (Sofia) ]
 Table of Contents:

1. Introduction
2. Romberg's method for setvalued mappings
3. Extrapolation method for the computation of reachable sets
©
Robert Baier
Last modified: Wed May 27 17:33:43 MDT 1998