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

作者：Kim Hongjoong^*; Kim Yoontae; Yoon Daeki

来源：Applied Mathematical Modelling, 2012, 36(7): 3074-3087.

DOI：10.1016/j.apm.2011.09.086

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

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.

• 出版日期2012-7