Overview

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. This monograph presents new probabilistic representations for classical boundary value problems of mathematical physics and is the first book devoted to the walk on boundary algorithms. Compared to the well-known Wiener and diffusion path integrals, the trajectories of random walks in this publication are simlated on the boundary of the domain as Markov chains generated by the kernels of the boundary integral equations equivalent to the original boundary value problem. The book opens with an introduction for solving the interior and exterior boundary values for the Laplace and heat equations, which is followed by applying this method to all main boundary value problems of the potential and elasticity theories.

Full Product Details

Author:   Karl K. Sabelfeld ,  Nikolai A. Simonov
Publisher:   Brill
Imprint:   VSP International Science Publishers
Edition:   Reprint 2012
Dimensions:   Width: 16.00cm , Height: 1.00cm , Length: 24.00cm
Weight:   0.390kg
ISBN:  

9789067641838

ISBN 10:   9067641839
Pages:   138
Publication Date:   October 1994
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Introduction RANDOM WALK ALGORITHMS FOR SOLVING INTEGRAL EQUATIONS Conventional Monte Carlo scheme Biased estimators Linear-fractional transformations and relations to iterative processes Asymptotically unbiased estimators based on singular approximation of the kernel Integral equation of the first kind RANDOM WALK ON BOUNDARY ALGORITHMS FOR SOLVING THELAPLACE EQUATION Newton potentials and boundary integral equations of the electrostatics The interior Dirichlet problem and isotropic Random Walk on Boundary process Solution of the Neumann problem Third boundary value problem and alternative methods of solving the Dirichlet problem Inhomogeneous problems Calculation of the derivatives near the boundary Normal derivative of a double layer potential WALK ON BOUNDARY ALGORITHMS FOR THE HEAT EQUATION Heat potential and Volterra boundary integral equations Nonstationary Walk on Boundary process The Dirichlet problem The Neumann problem Third boundary value problem Unbiasedness and variance of the Walk on Boundary algorithms The cost of the Walk on Boundary algorithms Inhomogeneous heat equation Calculation of derivatives on the boundary SPATIAL PROBLEMS OF ELASTICITY Elastopotentials and systems of boundary integral equations of the elasticity theory First boundary value problem and estimators for singular integrals Other boundary value problems for the Lame equations and regular integral equations VARIANTS OF THE RANDOM WALK ON BOUNDARY FOR SOLVING THE STATIONARY POTENTIAL PROBLEMS The Robin problem and the ergodic theorem Stationary diffusion equation with absorption Stabilization method Multiply connected domains RANDOM WALK ON BOUNDARY IN NON LINEAR PROBLEMS Nonlinear Poisson equation Boundary value problem for the Navier--Stokes equation Bibliography

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