An Introduction to Computational Stochastic PDEs
Gabriel J. Lord, Heriot-Watt University;
Catherine E. Powell, University of Manchester;
Tony Shardlow, University of Bath
Cambridge University Press, 2014
ISBN: 9780521728522;
Language: English
An Introduction to Computational Stochastic PDEs provides a comprehensive introduction to numerical methods, 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, discusses the Monte Carlo method, and introduces 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 text includes a set of downloadable MATLAB codes, allowing 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.
The text includes a set of downloadable MATLAB codes, allowing 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.
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