An Introduction to Computational Stochastic PDEs

An Introduction to Computational Stochastic PDEs by Gabriel J. Lord, published by Cambridge University Press on August 11, 2014, is a comprehensive resource that introduces numerical methods and analysis related to stochastic processes, random fields, and stochastic differential equations. This edition spans 520 pages and is presented in English, making it accessible for graduate students and researchers seeking to understand uncertainty quantification for risk analysis.

Readers will find a detailed exploration of traditional stochastic ordinary differential equations (ODEs) with white noise forcing, strong and weak approximation techniques, and the multi-level Monte Carlo method. The book also delves into the application of random fields to the numerical solution of elliptic partial differential equations (PDEs) with correlated random data, as well as the introduction of stochastic Galerkin finite-element methods. With a focus on practical applications in fields such as finance, mathematical biology, and fluid flow modeling, the text includes worked examples, exercises, and downloadable MATLAB codes to facilitate hands-on computation and problem-solving.