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Dependence of polynomial chaos on random types of forces of KdV equations. (English) Zbl 1252.60063

Summary: The 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.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)

Software:

Matlab
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References:

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