ENCLOSING SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS : WITH APPLICATIONS

Ole Stauning

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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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