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Generalized Polynomial Chaos For Stochastic Parabolic Equation

Posted on:2016-09-07Degree:MasterType:Thesis
Country:ChinaCandidate:N LiFull Text:PDF
GTID:2180330476950208Subject:Mathematics
Abstract/Summary:PDF Full Text Request
We discuss in this paper solvers for stochastic heat conduction equation and stochastic Allen-Cahn equation in random media, and the stochastic partial differential equation can turn into a set of coupled deterministic partial di?erential equations by using the polynomial chaos method. Here, we employ mixed ?rst order and second order explicit/implicit scheme in temporal and adopt fourier spectral method in spatial to solve the set of deterministic partial di?erential equations. For the stochastic heat conduction equation, the error of mean and variance will reach ?rst order accuracy and second order accuracy, respectively,and the two kinds of error getting smaller with the order of polynomial chaos increases. For the stochastic Allen-Cahn equation, we employ explicit scheme for the nonlinear term and the error of mean have ?rst order accuracy and second order accuracy, but the error of variance is not well. Moreover, numerical comparisons with the Monte Carlo method are reported, which demonstrates the e?ectivity and feasibility of the polynomial chaos method.
Keywords/Search Tags:Generalized polynomial chaos method, Stochastic heat conduction equation, Stochastic Allen-Cahn equation, Mixed explicit/implicit scheme, Fourier spectral method
PDF Full Text Request
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