An introduction to computational stochastic PDEs
"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…
Read More ↓Title Statements
- Full title :An introduction to computational stochastic PDEs / Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath.
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 modeling and materials science"--
Read More ↓Edition Statements
- Publication Date:2014.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:New York, NY, USA
- Language:eng
- Publication Date:2014.
The Physical Object
- Description:xi, 503 pages : : illustrations (some color) ; : 26 cm.
Edition Identifiers
- ISBN:9780521899901, 0521899907, 9780521728522, 0521728525, 1139898132, 9781139898133
- oclc:ocn868648659
- LC Classification:QA274.25
- Dewey Decimal:519.2/2
Table of Contents
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; 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs -- Exercises -- Appendix -- References -- Index.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Computermathematik
Mathematics for large scale computing
Mathematics for large scale computing
Introduction to parallel computing
Computer arithmetic and self-validating numerical methods
Computer arithmetic and self-validating numerical methods
Files & Downloads
-
An Introduction to Computational Stochastic PDEs …
PDF · 11.8 MB · updated
Rate & Review