  The paper presents a general strategy to solve ordinary differential
equations (ODE), where some coefficient depend on the spatial variable and on
additional random variables. The approach is based on the application of a
recently developed dimension-incremental sparse fast Fourier transform. Since
such algorithms require periodic signals, we discuss periodization strategies
and associated necessary deperiodization modifications within the occuring
solution steps.
  The computed approximate solutions of the ODE depend on the spatial variable
and on the random variables as well. Certainly, one of the crucial challenges
of the high dimensional approximation process is to rate the influence of each
variable on the solution as well as the determination of the relations and
couplings within the set of variables. The suggested approach meets these
challenges in a full automatic manner with reasonable computational costs,
i.e., in contrast to already existing approaches, one does not need to
seriously restrict the used set of ansatz functions in advance.
