### 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 |
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Pages (from-to) | 3080-3093 |

Number of pages | 14 |

Journal | Applied Mathematical Modelling |

Volume | 36 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2012 Jul |

### Keywords

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

### ASJC Scopus subject areas

- Modelling and Simulation
- Applied Mathematics

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## Cite this

*Applied Mathematical Modelling*,

*36*(7), 3080-3093. https://doi.org/10.1016/j.apm.2011.09.086