An Introduction to Computational Stochastic PDEs
Authors
Gabriel J. Lord (Heriot-Watt)Catherine E. Powell (Manchester)
Tony Shardlow (Bath)
Cambridge Texts in Applied Mathematics, CUP
Hardback (ISBN: 9780521899901)
Paperback (ISBN: 9780521728522)
and eBook.
To order :
- USA : Paperback Hardback eBook from CUP.
- UK : Paperback Hardback eBook from CUP
- Amazon: UK, FR, DE, USA.
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Review from MathSciNet
This book gives both accessible and extensive coverage on stochastic partial differential equations and their numerical solutions. It offers a well-elaborated background needed for solving numerically stochastic PDEs, both parabolic and elliptic. For the numerical solutions it presents not only proofs of convergence results of different numerical methods but also actual implementations, here in Matlab, with technical details included.
The book is self-contained, with the necessary theory thoroughly explained. It consists of three parts, divided into ten chapters. The first part covers deterministic differential equations and related numerical methods. Part Two gives necessary background on stochastic processes and random fields. The third part treats stochastic ordinary differential equations, elliptic PDEs with random coefficients, and semilinear parabolic stochastic PDEs with different numerical methods, such as different variations of Galerkin methods together with semi-implicit Euler approximations or the Milstein method. To each chapter are appended apt exercises.
With numerical implementations hard to find elsewhere in the literature, and a nice presentation of new research findings together with rich references, the book is a welcome companion for anyone working on numerical solutions of stochastic PDEs, and may also be suitable for use in a course on computational stochastic PDEs.