Monte Carlo Methods
Springer Berlin (Hersteller)
978-3-540-53001-5 (ISBN)
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Deals with random walk methods for solving multi-dimensional boundary value problems - Monte Carlo algorithms, which are constructed for three classes of problems - potential theory, elasticity and diffusion. Some advantages of new methods compared to conventional numerical methods are stressed.
This book deals with random walk methods for solving multi-dimensional boundary value problems. Monte Carlo algorithms are constructed for three classes of problems - potential theory, elasticity and diffusion. Some of the advantages of new methods as compared to conventional numerical methods are that they cater for stochasticities in the boundary value problems and complicated shapes of the boundaries. This monograph on mathematical physics, numerical and computational techniques, computer science and technology is intended for researchers and students in computational and applied mathematics, simulation and mathematical physics.
Contents: Introduction.- General Schemes for Constructing Scalar and Vector Monte Carlo Algorithms for Solving Boundary Value Problems: Random Walks on Boundary and Inside the Domain Algorithms. Random Walks and Approximations of Random Processes.- Monte Carlo Algorithms for Solving Integral Equations: Algorithms Based on Numerical Analytical Continuation. Asymptotically Unbiased Estimates Based on Singular Approximation of the Kernel. The Eigen-value Problems for the Integral Operators. Alternative Constructions of the Resolvent: Modifications and Numerical Experiments.- Monte Carlo Algorithms for Solving Boundary Value Problems of the Potential Theory: The Walk on Boundary Algorithms for Solving Interior and Exterior Boundary Value Problems of the Potential Theory. Walk Inside the Domain Algorithms.
Numerical Solution of Some Test and Applied Problems of Potential Theory in Determination and Stochastic Formulation.- Carlo Algorithms for Solving High-Order Equations and the Elasticity Problems: Biharmonic Problems. Metaharmonic Equations. Spatial Problems of the Elasticity Theory. Application to Stochastic Elasticity Problems.- Monte Carlo Algorithms for Solving Diffusion Problems: Walk on Boundary Algorithms for the Heat Equation. The Walk Inside the Domain Algorithms. Particle Diffusion in Random Velocity Fields. Applications to Diffusion Problems.- References.- Subject Index.
| Reihe/Serie | Springer Series in Computational Physics |
|---|---|
| Zusatzinfo | 62 figs. |
| Sprache | englisch |
| Gewicht | 594 g |
| Einbandart | gebunden |
| Schlagworte | Monte-Carlo-Methode • Randwertproblem |
| ISBN-10 | 3-540-53001-0 / 3540530010 |
| ISBN-13 | 978-3-540-53001-5 / 9783540530015 |
| Zustand | Neuware |
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