  We introduce PoCET: a free and open-scource Polynomial Chaos Expansion
Toolbox for Matlab, featuring the automatic generation of polynomial chaos
expansion (PCE) for linear and nonlinear dynamic systems with time-invariant
stochastic parameters or initial conditions, as well as several simulation
tools. It offers a built-in handling of Gaussian, uniform, and beta probability
density functions, projection and collocation-based calculation of PCE
coefficients, and the calculation of stochastic moments from a PCE. Efficient
algorithms for the calculation of the involved integrals have been designed in
order to increase its applicability. PoCET comes with a variety of introductory
and instructive examples. Throughout the paper we show how to perform a
polynomial chaos expansion on a simple ordinary differential equation using
PoCET, as well as how it can be used to solve the more complex task of optimal
experimental design.
