Title: Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional Pdes and Applications
Publisher: De Gruyter
Publication Date: 2016
Language: English
ISBN 10: 3110479060
ISBN 13: 9783110479065
Binding: Hardcover
Condition: Brand New
Weight: 0.54 kilograms

About this title

Synopsis

This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach.
The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics.

Contents:
Introduction
Random walk algorithms for solving integral equations
Random walk-on-boundary algorithms for the Laplace equation
Walk-on-boundary algorithms for the heat equation
Spatial problems of elasticity
Variants of the random walk on boundary for solving stationary potential problems
Splitting and survival probabilities in random walk methods and applications
A random WOS-based KMC method for electron–hole recombinations
Monte Carlo methods for computing macromolecules properties and solving related problems
Bibliography

About the Author

Karl K. Sabelfeld, Novosibirsk State University, Russia;
Nikolai A. Simonov, Novosibirsk State University, Russia.

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