Validated Solution of Initial Value Problems for ODEs with Interval Parameters
Youdong Lin, Mark A. Stadtherr · 2006
Abstract. In initial value problems for ODEs with interval-valued parameters, 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 several available software packages that deal with this case. However, relatively little work has been done on the case in which parameters are given by intervals. We demonstrate 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 numerical examples involving kinetics in a bioreactor and motion of a double pendulum.