Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Numerical Methods for Differential Equations in Random Domains
SIAM Journal on Scientific Computing
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System
SIAM Journal on Scientific Computing
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This paper deals with the error analysis of generalized polynomial chaos (gPC) for nonlinear random ordinary differential equations. The analysis shows that the global error mainly relies on the projection error and the numerical error. For the deterministic systems obtained from the gPC method, a kind of numerical approach with error analysis is given. At last, a numerical experiment is carried out to support the theoretical results.