Solving Spdes By A Least Squares Method

Hassan Manouzi
2014 Zenodo  
We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a
more » ... east square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.
doi:10.5281/zenodo.1336965 fatcat:4vyjpwzccbatnbokrszihhx4rq