  Uncertainty is unavoidable in modeling dynamical systems and it may be
represented mathematically by differential inclusions. In the past, we proposed
an algorithm to compute validated solutions of differential inclusions; here we
provide several theoretical improvements to the algorithm, including its
extension to piecewise constant and sinusoidal approximations of uncertain
inputs, updates on the affine approximation bounds and a generalized formula
for the analytical error. The approach proposed is able to achieve higher order
convergence with respect to the current state-of-the-art. We implemented the
methodology in Ariadne, a library for the verification of continuous and hybrid
systems. For evaluation purposes, we introduce ten systems from the literature,
with varying degrees of nonlinearity, number of variables and uncertain inputs.
The results are hereby compared with two state-of-the-art approaches to
time-varying uncertainties in nonlinear systems.
