Description: Stochastic Numerics for Mathematical Physics by Michael V. Tretyakov, Grigori Noah Milstein 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Notes This book contains much material never published before in book form Back Cover 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. Table of Contents 1 Mean-square approximation for stochastic differential equations.- 2 Weak approximation for stochastic differential equations.- 3 Numerical methods for SDEs with small noise.- 4 Stochastic Hamiltonian systems and Langevin-type equations.- 5 Simulation of space and space-time bounded diffusions.- 6 Random walks for linear boundary value problems.- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations.- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach.- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets.- A Appendix: Practical guidance to implementation of the stochastic numerical methods.- A.1 Mean-square methods.- A.2 Weak methods and the Monte Carlo technique.- A.3 Algorithms for bounded diffusions.- A.4 Random walks for linear boundary value problems.- A.5 Nonlinear PDEs.- A.6 Miscellaneous.- References. Review From the reviews of the first edition:"Milstein and Tretyakovs 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) Long Description 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. Review Text From the reviews of the first edition: "Milstein and Tretyakovs 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. a? 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) Review Quote From the reviews of the first edition:"Milstein and Tretyakovs 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) Feature This book contains much material never published before in book form Details ISBN3540211101 Author Grigori Noah Milstein Short Title STOCHASTIC NUMERICS FOR MATHEM Series Scientific Computation Language English ISBN-10 3540211101 ISBN-13 9783540211105 Media Book Format Hardcover Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Pages 596 DEWEY 530.15923 Illustrations XIX, 596 p. DOI 10.1007/b94626 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2004 ed. Year 2004 Edition 2004th Publication Date 2004-05-26 Alternative 9783642059308 Audience Professional & Vocational Replaced by 9783030820398 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96249994;
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ISBN-13: 9783540211105
Book Title: Stochastic Numerics for Mathematical Physics
Number of Pages: 596 Pages
Language: English
Publication Name: Stochastic Numerics for Mathematical Physics
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Publication Year: 2004
Subject: Mathematics, Physics
Item Height: 235 mm
Item Weight: 2290 g
Type: Textbook
Author: Grigori Noah Milstein, Michael V. Tretyakov
Item Width: 155 mm
Format: Hardcover
