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Robert Baier

Extrapolation Methods for the Computation of Set-Valued Integrals and Reachable Sets of Linear Differential Inclusions

The paper is published in:
ZAMM 74 (1994), No. 6, T555-557.
MSC:
93B03 Attainable sets
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections, See Also {26E25, 54C60, 54C65, 90A14}
34A60 Equations with multivalued right-hand sides, See Also
65L05 Initial value problems
65L06 Multistep, Runge-Kutta and extrapolation methods

Keywords:
extrapolation methods; set-valued integrals; linear differential inclusions

Abstract:
The following linear differential inclusion is considered:

\begin{displaymath} \dot y(t)\in (A(t) y(t)+ U(t)),\ y(a)\in Y_0,\ t\in [a,b], \end{displaymath}

where $Y_0 \subseteq \mathbb R^n$, A(.) is an integrable n x n-matrix function and U(.) is a measurable and integrably bounded set-valued 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 $y: [a,b]\to \mathbb R^n$, 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 set-valued mappings
3. Extrapolation method for the computation of reachable sets


© Robert Baier
Last modified: Wed May 27 17:33:43 MDT 1998