Solution of some semi-linear Dirichlet problem by Monte Carlo method
Abdujabar RasulovUniversity of World Economy and Diplomacy, UzbekistanGulnora RaimovaInstitute of Mathematics, Academy of Sciences of Uzbekistan, UzbekistanMatyokub BakoevUniversity of World Economy and Diplomacy, Uzbekistan
ABI
Abstract
In this paper, a Dirichlet boundary value problem (BVR) for semi-linear elliptic equation is considered. Assuming the existence of solution BVR we obtained a probabilistic representation of the solution as a mathematical expectation of some random variable. In accordance with a probabilistic representation were constructed on the trajectories of the branching random process unbiased estimator of the solution. An unbiased estimator of the solution has finite variance, based on the trajectories of a branching process with a finite average number of branchings. Some numerical experiments are performed.
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