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Extrapolation methods for the computation of set-valued integrals and reachable sets of linear differential inclusions. (English) Zbl 0816.93007

The following linear differential inclusion is considered: \[ \dot y(t)\in (A(t) y(t)+ U(t)),\;y(a)\in Y_ 0,\;t\in [a,b], \] where \(Y_ 0\subseteq \mathbb{R}^ n\), \(A(.)\) is an integrable \(n\times n\)-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.

MSC:

93B03 Attainable sets, reachability
34A60 Ordinary differential inclusions
65L05 Numerical methods for initial value problems involving ordinary differential equations
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