TY - BOOK ID - 78343969 TI - Stochastic Methods for Boundary Value Problems AU - Sabelfeld, Karl K., AU - Simonov, Nikolai A PY - 2016 SN - 3110479168 3110479451 9783110479454 9783110479454 9783110479164 3110479060 9783110479065 PB - Berlin Boston DB - UniCat KW - Boundary value problems KW - Stochastic analysis. KW - Random walks (Mathematics) KW - Additive process (Probability theory) KW - Random walk process (Mathematics) KW - Walks, Random (Mathematics) KW - Stochastic processes KW - Analysis, Stochastic KW - Mathematical analysis KW - Numerical solutions. UR - https://www.unicat.be/uniCat?func=search&query=sysid:78343969 AB - 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:IntroductionRandom walk algorithms for solving integral equationsRandom walk-on-boundary algorithms for the Laplace equationWalk-on-boundary algorithms for the heat equationSpatial problems of elasticityVariants of the random walk on boundary for solving stationary potential problemsSplitting and survival probabilities in random walk methods and applicationsA random WOS-based KMC method for electron-hole recombinationsMonte Carlo methods for computing macromolecules properties and solving related problemsBibliography ER -