An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations

@article{Ma2009AnAH,
  title={An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations},
  author={Xiang Ma and Nicholas Zabaras},
  journal={J. Comput. Physics},
  year={2009},
  volume={228},
  pages={3084-3113}
}
In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to SSFEM. It approximates the solution in the stochastic space using Lagrange polynomial interpolation… CONTINUE READING
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