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Titlebook: Numerical Methods for Stochastic Partial Differential Equations with White Noise; Zhongqiang Zhang,George Em Karniadakis Book 2017 Springe

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發(fā)表于 2025-3-21 18:29:26 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Numerical Methods for Stochastic Partial Differential Equations with White Noise
編輯Zhongqiang Zhang,George Em Karniadakis
視頻videohttp://file.papertrans.cn/670/669096/669096.mp4
概述Includes both theoretical and computational exercises, allowing for use with mixed-level classes.Provides Matlab codes for examples.The first book to emphasizes the Wong-Zakai approximation.Offers an
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Numerical Methods for Stochastic Partial Differential Equations with White Noise;  Zhongqiang Zhang,George Em Karniadakis Book 2017 Springe
描述.This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations
出版日期Book 2017
關(guān)鍵詞Nonlinear Stochastic Differential Equations; Wong-Zakai Approximation; Deterministic Integration Metho
版次1
doihttps://doi.org/10.1007/978-3-319-57511-7
isbn_softcover978-3-319-86181-4
isbn_ebook978-3-319-57511-7Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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978-3-319-86181-4Springer International Publishing AG 2017
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Numerical methods for stochastic differential equations,In this chapter, we discuss some basic aspects of stochastic differential equations (SDEs) including stochastic ordinary (SODEs) and partial differential equations (SPDEs).
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Wiener chaos methods for linear stochastic advection-diffusion-reaction equationsIn 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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Prologue,presenting various scales in particle simulations at molecular and mesoscopic scales, as well as extrinsic uncertainty, e.g., stochastic external forces, stochastic initial conditions, or stochastic boundary conditions.
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