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Full Description
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
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 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. Walk Inside the Domain Algorithms. Numerical Solution of Test and Applied Problems of Potential Theory in Deterministic. Monte Carlo Algorithms for Solving High-order Equations and Problems in Elasticity: Biharmonic Problem. Metaharmonic Equations. Spatial Problems of Elasticity Theory. Applications to Stochastic Elasticity Problems. 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.
