%0 Journal Article %A Audouze , Christophe %A Nair, Prasanth B. %D 2016 %I Begell House %K randomly parametrized ordinary differential equations, generalized polynomial chaos expansions, stochastic Galerkin projection schemes, a priori error estimates, temporal discretization error, stochastic structural dynamics %N 4 %P 287-312 %R 10.1615/Int.J.UncertaintyQuantification.2016015843 %T A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS %U https://www.dl.begellhouse.com/journals/52034eb04b657aea,55c0c92f02169163,2bb5e03d09701c8b.html %V 6 %X Generalized polynomial chaos (gPC) based stochastic Galerkin methods are widely used to solve randomly parametrized ordinary differential equations (RODEs). These RODEs are parametrized in terms of a finite number of independent and identically distributed second-order random variables. In this paper, we derive a priori error estimates for stochastic Galerkin approximations of RODEs accounting for the temporal and stochastic discretization errors. Under appropriate stochastic regularity assumptions, convergence rates are provided for first-order linear RODE systems and first-order nonlinear scalar RODEs. We also consider the case of second-order linear RODE systems that are routinely encountered in stochastic structural dynamics applications. Finally, some insights into the long-time behavior of gPC schemes are provided for a model problem drawing on the present analysis. %8 2016-11-07