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

Hongjoong Kim; Yoontae Kim; Daeki Yoon

doi:10.1016/j.apm.2011.09.086

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

Hongjoong Kim, Yoontae Kim, Daeki Yoon

Research output: Contribution to journal › Article › peer-review

8 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 language	English
Pages (from-to)	3080-3093
Number of pages	14
Journal	Applied Mathematical Modelling
Volume	36
Issue number	7
DOIs	https://doi.org/10.1016/j.apm.2011.09.086
Publication status	Published - 2012 Jul

Bibliographical note

Funding Information:
This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2010–0012584 ).

Keywords

KdV equation
Polynomial chaos
Spectral method
Stochastic differential equation

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

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10.1016/j.apm.2011.09.086

Cite this

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title = "Dependence of polynomial chaos on random types of forces of KdV equations",

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.",

keywords = "KdV equation, Polynomial chaos, Spectral method, Stochastic differential equation",

author = "Hongjoong Kim and Yoontae Kim and Daeki Yoon",

note = "Funding Information: This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2010–0012584 ). ",

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AU - Kim, Hongjoong

AU - Kim, Yoontae

AU - Yoon, Daeki

N1 - Funding Information: This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2010–0012584 ).

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

KW - KdV equation

KW - Polynomial chaos

KW - Spectral method

KW - Stochastic differential equation

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M3 - Article

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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