Abstract:
We consider numerical methods for finding approximate solutions
to Ordinary Differential Equations (ODEs) with parameters distributed
with some probability by the Generalized Polynomial Chaos (GPC)
approach. In particular, we consider those with forcing functions that
have a random parameter in both the scalar and vector case. We then
consider linear systems of ODEs with deterministic forcing and randomness
in the matrix of the systems and conclude with a method
of approximating solutions to the case where the system involves a
nonlinear function of a matrix and a random variable.
