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Stochastic Numerics for Mathematical Physics

Author: G N Milʹshteĭn; Michael V Tretyakov
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004.
Series: Scientific computation.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: G N Milʹshteĭn; Michael V Tretyakov
ISBN: 9783662100639 3662100630
OCLC Number: 851382445
Description: 1 online resource (xix, 596 pages).
Contents: Mean-Square Approximation for Stochastic Differential Equations --
Weak Approximation for Stochastic Differential Equations --
Numerical Methods for SDEs with Small Noise --
Stochastic Hamiltonian Systems and Langevin Type Equations --
Simulation of Space and Space-Time Bounded Diffusions --
Random Walks for Linear Boundary Value Problems --
Probabilistic Approach to Numerical Solution of the Cauchy Problem for Nonlinear Parabolic Equations --
Numerical Solution of the Nonlinear Dirichlet and Neumann Problems Based on the Probabilistic Approach --
Application of Stochastic Numerics to Models with Stochastic Resonance and to Brownian Ratchets --
Appendix: Practical Guidance to Implementation of the Stochastic Numerical Methods --
References --
Index.
Series Title: Scientific computation.
Responsibility: by Grigori N. Milstein, Michael V. Tretyakov.

Abstract:

In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear.  Read more...

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From the reviews of the first edition:"Milstein and Tretyakov's book is a significant contribution to stochastic numerics. It is essential reading for anyone with serious interest in the field, Read more...

 
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