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Wiener chaos methods for linear stochastic advection-diffusion-reaction equations

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Numerical Methods for Stochastic Partial Differential Equations with White Noise

Part of the book series: Applied Mathematical Sciences ((AMS,volume 196))

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Abstract

In this chapter, we discuss numerical algorithms using Wiener chaos expansion (WCE) for solving second-order linear parabolic stochastic partial differential equations (SPDEs). The algorithm for computing moments of the SPDE solutions is deterministic, i.e., it does not involve any statistical errors from generating random numbers.

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Notes

  1. 1.

    Matlab R2010b was used for each test on a single core of two Intel Xeon 5540 (2.53 GHz) quad-core Nehalem processors.

  2. 2.

    This is an estimated time according to the tests with smaller Δt, L and with M = 100.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts, USA

    Zhongqiang Zhang

  2. Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

    George Em Karniadakis

Authors
  1. Zhongqiang Zhang
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  2. George Em Karniadakis
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Zhang, Z., Karniadakis, G.E. (2017). Wiener chaos methods for linear stochastic advection-diffusion-reaction equations. In: Numerical Methods for Stochastic Partial Differential Equations with White Noise. Applied Mathematical Sciences, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-57511-7_6

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