TY - JOUR

T1 - Dependence of polynomial chaos on random types of forces of KdV equations

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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U2 - 10.1016/j.apm.2011.09.086

DO - 10.1016/j.apm.2011.09.086

M3 - Article

AN - SCOPUS:84858334190

VL - 36

SP - 3080

EP - 3093

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 7

ER -