Dependence of polynomial chaos on random types of forces of KdV equations

Hongjoong Kim, Yoontae Kim, Daeki Yoon

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this study, one-dimensional stochastic Korteweg-de Vries equation with uncertainty in its forcing term is considered. Extending the Wiener chaos expansion, a numerical algorithm based on orthonormal polynomials from the Askey scheme is derived. Then dependence of polynomial chaos on the distribution type of the random forcing term is inspected. It is numerically shown that when Hermite (Laguerre or Jacobi) polynomial chaos is chosen as a basis in the Gaussian (Gamma or Beta, respectively) random space for uncertainty, the solution to the KdV equation converges exponentially. If a proper polynomial chaos is not used, however, the solution converges with slower rate.

Original languageEnglish
Pages (from-to)3080-3093
Number of pages14
JournalApplied Mathematical Modelling
Volume36
Issue number7
DOIs
Publication statusPublished - 2012 Jul 1

Fingerprint

Polynomial Chaos
KdV Equation
Chaos theory
Forcing Term
Polynomials
Converge
Orthonormal Polynomials
Chaos Expansion
Uncertainty
Laguerre Polynomials
Hermite Polynomials
Jacobi Polynomials
Korteweg-de Vries equation
Korteweg-de Vries Equation
Numerical Algorithms
Stochastic Equations

Keywords

  • KdV equation
  • Polynomial chaos
  • Spectral method
  • Stochastic differential equation

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation

Cite this

Dependence of polynomial chaos on random types of forces of KdV equations. / Kim, Hongjoong; Kim, Yoontae; Yoon, Daeki.

In: Applied Mathematical Modelling, Vol. 36, No. 7, 01.07.2012, p. 3080-3093.

Research output: Contribution to journalArticle

Kim, Hongjoong ; Kim, Yoontae ; Yoon, Daeki. / Dependence of polynomial chaos on random types of forces of KdV equations. In: Applied Mathematical Modelling. 2012 ; Vol. 36, No. 7. pp. 3080-3093.
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