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Scientific Computation

Stochastic Numerics for Mathematical Physics

Authors: Milstein, Grigori Noah, Tretyakov, Michael V.

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eBook £93.50
price for United Kingdom (gross)
valid through October 16, 2017
  • ISBN 978-3-662-10063-9
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  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £117.00
price for United Kingdom (gross)
valid through October 16, 2017
  • ISBN 978-3-540-21110-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £117.00
price for United Kingdom (gross)
  • ISBN 978-3-642-05930-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

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)


Table of contents (9 chapters)

  • Mean-square approximation for stochastic differential equations

    Milstein, Grigori N. (et al.)

    Pages 1-82

  • Weak approximation for stochastic differential equations

    Milstein, Grigori N. (et al.)

    Pages 83-170

  • Numerical methods for SDEs with small noise

    Milstein, Grigori N. (et al.)

    Pages 171-210

  • Stochastic Hamiltonian systems and Langevin-type equations

    Milstein, Grigori N. (et al.)

    Pages 211-282

  • Simulation of space and space-time bounded diffusions

    Milstein, Grigori N. (et al.)

    Pages 283-338

Buy this book

eBook £93.50
price for United Kingdom (gross)
valid through October 16, 2017
  • ISBN 978-3-662-10063-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £117.00
price for United Kingdom (gross)
valid through October 16, 2017
  • ISBN 978-3-540-21110-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £117.00
price for United Kingdom (gross)
  • ISBN 978-3-642-05930-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Numerics for Mathematical Physics
Authors
Series Title
Scientific Computation
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-3-662-10063-9
DOI
10.1007/978-3-662-10063-9
Hardcover ISBN
978-3-540-21110-5
Softcover ISBN
978-3-642-05930-8
Series ISSN
1434-8322
Edition Number
1
Number of Pages
XIX, 596
Topics