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Stochastic Numerics for Mathematical Physics : Scientific Computation - Grigori Noah Milstein

Stochastic Numerics for Mathematical Physics

Scientific Computation


Published: 26th May 2004
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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 propose many new special schemes, some published here for the first time. 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. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

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, either theoretical or practical." (Mathematical Reviews, 2005)

"The monograph presents research results of the authors concerning the numerical treatment of stochastic differential equations. ... The book is written in the style of a research exposition. It provides a rich source of mathematical theory, examples and insightful remarks and is thus essential material for those who are interested in the subject, from both a theoretical and practical viewpoint." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1085, 2006)

Mean-square approximation for stochastic differential equationsp. 1
Weak approximation for stochastic differential equationsp. 83
Numerical methods for SDEs with small noisep. 171
Stochastic Hamiltonian systems and Langevin-type equationsp. 211
Simulation of space and space-time bounded diffusionsp. 283
Random walks for linear boundary value problemsp. 339
Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equationsp. 407
Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approachp. 461
Application of stochastic numerics to models with stochastic resonance and to Brownian ratchetsp. 509
Practical guidance to implementation of the stochastic numerical methodsp. 541
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540211105
ISBN-10: 3540211101
Series: Scientific Computation
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 596
Published: 26th May 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.33
Weight (kg): 2.29