An Introduction to Computational Stochastic PDEs

Book Name : An Introduction to Computational Stochastic PDEs

By by Gabriel J. Lord, Catherine E. Powell, Tony Shardlow

Sub Title : NA

Written by : by Gabriel J. Lord, Catherine E. Powell, Tony Shardlow

Subject Category : Language Arts & Disciplines

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about this book

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. Cambridge University Press; August 2014 ISBN 9781139898133 Read online, or download in secure PDF or secure EPUB format Title: An Introduction to Computational Stochastic PDEs Author: Gabriel J. Lord; Catherine E. Powell; Tony Shardlow Imprint: Cambridge University Press Subject categories Language Arts & Disciplines > Communication Mathematics > Differential Equations Business > Finance Computers > Mathematical & Statistical Software Mathematics > Probability & Statistics Business > Risk Management ISBNs 9780521899901 9781139898133 9781139904087 In The Press '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, Mathematical Reviews

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Related subjects

Language Arts & Disciplines - Communication Mathematics - Differential Equations Business - Finance Computers - Mathematical & Statistical Software Mathematics - Probability & Statistics Business - Risk Management

ISBN

9780521899901 - 9781139898133 - 9781139904087

In The Press:

'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, Mathematical Reviews

Imprint

Cambridge University Press

 

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