| 书目名称 | Numerical Methods for Stochastic Partial Differential Equations with White Noise |
| 编辑 | Zhongqiang Zhang,George Em Karniadakis |
| 视频video | |
| 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 |
| 丛书名称 | Applied Mathematical Sciences |
| 图书封面 |  |
| 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 |
| 关键词 | Nonlinear Stochastic Differential Equations; Wong-Zakai Approximation; Deterministic Integration Metho |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-57511-7 |
| isbn_softcover | 978-3-319-86181-4 |
| isbn_ebook | 978-3-319-57511-7Series ISSN 0066-5452 Series E-ISSN 2196-968X |
| issn_series | 0066-5452 |
| copyright | Springer International Publishing AG 2017 |
发表于 2025-3-21 18:29:26
