## Scanned old papers

Poincaré H.,

**Sur certaines solutions particulières du problème des trois corps**,

Comptes rendus de l'Académie des sciences, volume 97, pages 251-252, 1883.

page 251, page 252

*Comment: there is the first formulation of the famous Poincaré-Miranda theorem. Poincaré's work remained unknown during approximately ninety years. Unaware of this work, Brouwer proposed his fixed point theorem in 1909 and Miranda proved the equivalence between the Poincaré-Miranda theorem and the Brouwer fixed point theorem in 1941. Poincaré's work has been re-discovered in the 70's. Poincaré's fifteen-word-sketch-of-the-proof seems to show that he had in mind arguments close to the ones proposed in M.N. Vrahatis, A short proof and a generalization of Miranda's existence theorem Proceedings of the American Mathematical Society, 107, No. 3, 701-703, (1989).*

Kruckeberg F.,

**Ordinary differential equations**,

In, E. Hansen, editor, Topics in Interval Analysis, pages 91-93, Oxford University Press, 1969.

(2285K)

*Comment: there is an actual parallelepiped method for the approximation of the solution to IVP for ODE. Kruckeberg also mentions inner approximation, though no hint is given on the inner approximation process.*

Lohner R. J.,

**Computation of Guaranteed Enclosures for the Solutions of Ordinary Initial and Boundary Value Problems**,

In, J. R. Cash and I. Gladwell, editors, Computational Ordinary Differential Equations, pages 425-436, Clarendon Press, 1992.

(450K)

*Comment: Lohner presents there the promizing interval shooting and multiple-shooting methods.*

Ortolf H. J.,

**Eine Verallgemeinerung der Intervallarithmetik**,

Gesellschaft für Mathematik und Datenverarbeitung, 1969.

(2800K)