Solution of dirichlet's problem for Laplace's equation by the method of statistical tests

Abstract

BELOW it is shown that the solution of the internal and external Dirichlet problems for Laplace's equation may be obtained by the method of statistical tests if the region of definition of the solution is presented in the form of the superposition of partially intersecting subregions for which the solution is known. According to the given boundary conditions the required solution is defined in terms of probability characteristics of the Markov process of random transitions between points of the boundaries of the subregions. Examples of the practical application of the method of statistical tests in solving Dirichlet problems are given.