The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen- sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi- cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent...

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

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.