Gabriel J. Lord

Introduction to Computational Stochastic PDEs (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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(R) 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 11. August 2014
• Englisch
• ISBN-13: 9781139904087
• Artikelnr.: 41329618

Autorenporträt

Gabriel Lord is a Professor in the Maxwell Institute, Department of Mathematics, at Heriot-Watt University, Edinburgh. He has worked on stochastic PDEs and applications for the past ten years. He is the co-editor of Stochastic Methods in Neuroscience with C. Liang, has organised a number of international meetings in the field, and is principal investigator on the porous media processes and mathematics network funded by the Engineering and Physical Sciences Research Council (UK). He is a member of the Society for Industrial and Applied Mathematics, LMS, and EMS, as well as an Associate Editor for the SIAM Journal on Scientific Computing and the SIAM/ASA Journal on Uncertainty Quantification.

Inhaltsangabe

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.