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Towards High-order Methods for Stochastic Di erential ...

Towards High-order Methods for Stochastic DifferentialEquations with White Noise: A Spectral ApproachbyZhongqiang ZhangA dissertation submitted in partial fulfillment of therequirements for the degree of Doctor of Philosophyin the Division of Applied Mathematics at Brown UniversityPROVIDENCE, RHODE ISLANDMay 2014 Abstract of Towards High-order Methods for Stochastic Differential equations with White Noise:A Spectral Approach by Zhongqiang Zhang, , Brown University, May 2014We develop a recursive multistage Wiener chaos expansion method (WCE) and a recursive multi-stage Stochastic collocation method (SCM) for numerical integration of linear Stochastic advection-diffusion-reaction equations with multiplicative white noise.

Towards High-order Methods for Stochastic Di erential Equations with White Noise: A Spectral Approach by Zhongqiang Zhang A dissertation submitted in partial ful llment of the

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