Introduction to Computational Stochastic PDEs

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

Research output: Book/ReportBook

130 Citations (Scopus)

Abstract

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 modeling and materials science.
Original languageEnglish
Place of PublicationNew York, U. S. A.
PublisherCambridge University Press
Number of pages509
Edition1
ISBN (Print)9780521899901
DOIs
Publication statusPublished - 1 Jul 2014

Publication series

NameCambridge Texts in Applied Mathematics
No.50

Fingerprint

Stochastic PDEs
Monte Carlo method
Random Field
Mathematical Biology
Weak Approximation
Uncertainty Quantification
Parabolic PDEs
Multilevel Methods
Strong Approximation
Elliptic PDE
Galerkin Finite Element Method
Materials Science
Neuroscience
Risk Analysis
Finance
White noise
Computational Methods
Exercise
Forcing
Test Problems

Cite this

Lord, G. J., Powell, C. E., & Shardlow, T. (2014). Introduction to Computational Stochastic PDEs. (1 ed.) (Cambridge Texts in Applied Mathematics; No. 50). New York, U. S. A.: Cambridge University Press. https://doi.org/10.1017/CBO9781139017329

Introduction to Computational Stochastic PDEs. / Lord, Gabriel J.; Powell, Catherine E.; Shardlow, Tony.

1 ed. New York, U. S. A. : Cambridge University Press, 2014. 509 p. (Cambridge Texts in Applied Mathematics; No. 50).

Research output: Book/ReportBook

Lord, GJ, Powell, CE & Shardlow, T 2014, Introduction to Computational Stochastic PDEs. Cambridge Texts in Applied Mathematics, no. 50, 1 edn, Cambridge University Press, New York, U. S. A. https://doi.org/10.1017/CBO9781139017329
Lord GJ, Powell CE, Shardlow T. Introduction to Computational Stochastic PDEs. 1 ed. New York, U. S. A.: Cambridge University Press, 2014. 509 p. (Cambridge Texts in Applied Mathematics; 50). https://doi.org/10.1017/CBO9781139017329
Lord, Gabriel J. ; Powell, Catherine E. ; Shardlow, Tony. / Introduction to Computational Stochastic PDEs. 1 ed. New York, U. S. A. : Cambridge University Press, 2014. 509 p. (Cambridge Texts in Applied Mathematics; 50).
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