Monte Carlo Methods

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.