Paperback. 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. This comprehensive introduction to stochastic partial differential equations incorporates the effects of randomness into real-world models, offering graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. MATLAB codes are included, so that readers can perform computations themselves and solve the test problems discussed. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

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Detalles bibliogr�ficos

T�tulo

Introduction to Computational Stochastic Pdes (Paperback)

Editor

Cambridge University Press, Cambridge

Fecha de publicaci�n

2014

Idioma

Ingl�s

ISBN 10

0521728525

ISBN 13

9780521728522

Encuadernaci�n

Paperback

Estado

new

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Sinopsis

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.

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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.

Catherine Powell is a Senior Lecturer in Applied Mathematics and Numerical Analysis at the University of Manchester. She has worked in the field of stochastic PDEs and uncertainty quantification for ten years. She has co-organised several conferences on the subject, and together with Tony Shardlow, initialised the annual NASPDE series of meetings (now in its sixth year). Currently, she is the principal investigator on an Engineering and Physical Sciences Research Council funded project on the 'Numerical Analysis of PDEs with Random Data'. She is a member of the Society for Industrial and Applied Mathematics and an Associate Editor for the SIAM/ASA Journal on Uncertainty Quantification.

Tony Shardlow has been working in the numerical analysis group at the University of Bath since 2012. Before that, he held appointments at the universities of Manchester, Durham, Oxford, and Minnesota. He completed his Ph.D. in Scientific Computing and Computational Mathematics at Stanford University in 1997.

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