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
