<電子ブック>
Stochastic Numerics for Mathematical Physics

責任表示
著者
本文言語
出版者
出版年
出版地
関連情報
概要 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 s...olution 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.続きを見る
目次 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.
続きを見る
本文を見る Full text available from SpringerLink ebooks - Physics and Astronomy (Archive)

詳細

レコードID
主題
SSID
eISBN
登録日 2020.06.27
更新日 2020.06.28