Numerical Methods For Stochastic Partial Differential Equations With White Noise at Meripustak

Numerical Methods For Stochastic Partial Differential Equations With White Noise

Books from same Author: ZHANG Z

Books from same Publisher: SPRINGER

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  • General Information  
    Author(s)ZHANG Z
    PublisherSPRINGER
    ISBN9783319575100
    Pages394
    BindingHardbound
    LanguageEnglish
    Publish YearSeptember 2017

    Description

    SPRINGER Numerical Methods For Stochastic Partial Differential Equations With White Noise by ZHANG Z

    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 as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In add.