1. A method for propagating the state of an object and an uncertainty associated with the state of the object, the method comprising: receiving, by a computer system, an interval of time over which the uncertainty is to be propagated, as well as an ensemble of initial conditions that characterize the initial uncertainty associated with the state of an object and an ordinary differential equation (ODE) describing dynamics of the state of the object, which together define an initial value problem (IVP) ensemble, for the object, the IVP ensemble comprising a plurality of IVPs; solving, by the computer system, the IVPs in the IVP ensemble wherein the solution of one or more of the IVPs in the IVP ensemble depends upon the solution of one or more of the other IVPs in the IVP ensemble; characterizing, by the computer system, the uncertainty associated with the state of the object at the end of the time interval based on solving the IVPs in the IVP ensemble.