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  3. An Introduction to Computational Stochastic PDEs
  • Cited by 223
Publisher:
Cambridge University Press
Online publication date:
July 2014
Print publication year:
2014
Online ISBN:
9781139017329
DOI:
https://doi.org/10.1017/CBO9781139017329
Subjects:
Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Applied Probability and Stochastic Networks, Statistics and Probability
Series:
Cambridge Texts in Applied Mathematics (50)
Information

Book description

This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

Reviews

'This book gives both accessible and extensive coverage on stochastic partial differential equations and their numerical solutions. It offers a well-elaborated background needed for solving numerically stochastic PDEs, both parabolic and elliptic. For the numerical solutions it presents not only proofs of convergence results of different numerical methods but also actual implementations, here in Matlab, with technical details included … With numerical implementations hard to find elsewhere in the literature, and a nice presentation of new research findings together with rich references, the book is a welcome companion for anyone working on numerical solutions of stochastic PDEs, and may also be suitable for use in a course on computational stochastic PDEs.'

Roger Pettersson Source: Mathematical Reviews

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Contents

Contents
References
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