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An introduction to computational stochastic PDEs / Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath

Author
Lord, Gabriel J.
Published
Cambridge : Cambridge University Press, 2014.
Physical Description
1 online resource (xi, 503 pages) : digital, PDF file(s).
Additional Creators
Powell, Catherine E. and Shardlow, Tony
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Series
Contents
Machine generated contents note: Part I. Deterministic Differential Equations: 1. Linear analysis; 2. Galerkin approximation and finite elements; 3. Time-dependent differential equations; Part II. Stochastic Processes and Random Fields: 4. Probability theory; 5. Stochastic processes; 6. Stationary Gaussian processes; 7. Random fields; Part III. Stochastic Differential Equations: 8. Stochastic ordinary differential equations (SODEs); 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs.
Summary
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.
Subject(s)
ISBN
9781139017329 (ebook)
9780521899901 (hardback)
9780521728522 (paperback)
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
View MARC record | catkey: 34833080