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Generalized Polynomial Chaos Solution of Differential Equations with Random Inputs

by G. E. Karniadakis and C.-H. Su and D. Xiu and D. Lucor and Ch. Schwab and R. A. Todor

(Report number 2005-01)

Abstract
Stochastic modeling by differential equations with random inputs is reviewed. Recent developments in solution algorithms based on generalizations of the homogeneous Hermite Polynomial Chaos (PC) expansions of N. Wiener and on sparse tensor product approximations of spatial correlation functions in perturbation expansions are presented. Mathematical issues in the formulation, PC discretization, and numerical analysis of PC solution algorithms are discussed.

Keywords: Polynomial chaos, orthogonal polynomials, random inputs, differential equations, noisy systems, uncertainty quantification

@Techreport{KSXLST05_81,
  author = {G. E. Karniadakis and C.-H. Su and D. Xiu and D. Lucor and Ch. Schwab and R. A. Todor},
  title = {Generalized Polynomial Chaos Solution of Differential Equations with Random Inputs},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2005-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2005/2005-01.pdf },
  year = {2005}
}

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