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国际不确定性的量化期刊
影响因子: 3.259 5年影响因子: 2.547 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2016015843
pages 287-312

A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS

Christophe Audouze
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Ontario, Canada M3H 5T6
Prasanth B. Nair
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Ontario, Canada M3H 5T6

ABSTRACT

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.


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