## ENCLOSING SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS : WITH APPLICATIONS

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## Abstract

This report describes the method used in the program AWA
(German: AnfangsWertAufgaben ) which was developed by Rudolf Lohner.
The program is capable of solving ordinary differential equations,
obtaining verified bounds of the true solution.
Picard iterations are used to prove existence and to find a rough
enclosure of the solution, this rough enclosure are then sharpened
by Taylor expansion. Using a mean value method and Taylor expansion
of the variational equation, global errors are propagated.
A program package, DTU AWA, has been developed in C++ using the interval
packages PROFIL/BIAS. The program uses basically the same method as in
the original AWA, but in DTU AWA a precompiler is used to generate the
recursive code which is used in the integration to calculate the Taylor
coefficients.

## IMM Technical Report 18/96

Last modified August 21, 1996

Finn Kuno Christensen
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