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In this paper, we introduce a numerical solution of a stochastic partialdifferential equation (SPDE) of elliptic type using polynomial chaos along sidewith polynomial approximation at Sinc points. These Sinc points are defined bya conformal map and when mixed with the polynomial interpolation, it yields anaccurate approximation. The first step to solve SPDE is to use stochasticGalerkin method in conjunction with polynomial chaos, which implies a system ofdeterministic partial differential equations to be solved. The main difficultyis the higher dimensionality of the resulting system of partial differentialequations. The idea here is to solve this system using a small number ofcollocation points. Two examples are presented, mainly using Legendrepolynomials for stochastic variables. These examples illustrate that we requireto sample at few points to get a representation of a model that is sufficientlyaccurate.

Poly-Sinc Solution of Stochastic Elliptic Differential Equations