Stochastic Numerics for Mathematical Physics
By: by Grigori N. Milstein, Michael V. Tretyakov
Contributors: Tretyakov, Michael V.
Series: Scientific Computation; Scientific Computation
Publisher: Springer Berlin Heidelberg
Published: 2004
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 596
ISBN-13: 9783642059308; 9783662100639
Subjects: Distribution (Probability theory); Physics; Numerical analysis; Computer science
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.
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Table of contents: title: Mean-Square Approximation for Stochastic Differential Equations; title: Weak Approximation for Stochastic Differential Equations; title: Numerical Methods for SDEs with Small Noise; title: Stochastic Hamiltonian Systems and Langevin Type Equations; title: Simulation of Space and Space-Time Bounded Diffusions; title: Random Walks for Linear Boundary Value Problems; title: Probabilistic Approach to Numerical Solution of the Cauchy Problem for Nonlinear Parabolic Equations; title: Numerical Solution of the Nonlinear Dirichlet and Neumann Problems Based on the Probabilistic Approach; title: Application of Stochastic Numerics to Models with Stochastic Resonance and to Brownian Ratchets; title: Appendix: Practical Guidance to Implementation of the Stochastic Numerical Methods; title: References; title: Index.