WASET

	%0 Journal Article
	%A Hassan Manouzi and  Taous-Meriem Laleg-Kirati
	%D 2014
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 89, 2014
	%T Solving Stochastic Eigenvalue Problem of Wick Type
	%U https://publications.waset.org/pdf/9998205
	%V 89
	%X In this paper we study mathematically the eigenvalue
problem for stochastic elliptic partial differential equation of Wick
type. Using the Wick-product and the Wiener-It&ocirc; chaos expansion,
the stochastic eigenvalue problem is reformulated as a system of an
eigenvalue problem for a deterministic partial differential equation
and elliptic partial differential equations by using the Fredholm
alternative. To reduce the computational complexity of this system,
we shall use a decomposition method using the Wiener-It&ocirc; chaos
expansion. Once the approximation of the solution is performed using
the finite element method for example, the statistics of the numerical
solution can be easily evaluated.

	%P 753 - 756