Validated solutions of initial value problems for parametric ODEs

Authors:
Youdong Lin;Mark A. Stadtherr
Affiliations:
Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA;Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

In initial value problems for ODEs with interval-valued parameters and/or initial values, it is desirable in many applications to be able to determine a validated enclosure of all possible solutions to the ODE system. Much work has been done for the case in which initial values are given by intervals, and there are available software packages that deal with this case. However, less work has been done on the case in which parameters are given by intervals. We describe here a new method for obtaining validated solutions of initial value problems for ODEs with interval-valued parameters. The method also accounts for interval-valued initial values. The effectiveness of the method is demonstrated using several numerical examples involving parametric uncertainties.