Stochastic numerics for mathematical physics

Grigori N. Milstein, Michael V. Tretyakov - Collection Scientific computation

596 pages, parution le 10/06/2004

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Résumé

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.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Grigori N. Milstein, Michael V. Tretyakov
Collection	Scientific computation
Parution	10/06/2004
Nb. de pages	596
Format	16 x 24
Couverture	Relié
Poids	1020g
Intérieur	Noir et Blanc
EAN13	9783540211105