caa a22 4500 378939963 CHVBK 20180305123649.0 cr unu---uuuuu 161128e20041001xx s 000 0 eng 10.1515/1569398042395989 doi (NATIONALLICENCE)gruyter-10.1515/1569398042395989 Probabilistic representation and Monte Carlo methods for the first boundary value problem for a polyharmonic equation [Elektronische Daten] [V. L. Lukinov, G. A. Mikhailov] In this paper we give the results obtained by the constructed probabilistic representation of the solution to the first boundary value problem for a polyharmonic equation. It is shown that this solution is expressed by the parametric derivative of the solution to the specially constructed Dirichlet problem for the Helmholtz equation. On this basis we develop new algorithms of 'walk on a grid' and 'random walk by spheres' for the solution of a polyharmonic equation. Copyright 2004, Walter de Gruyter Lukinov V. L. Institute of Computational Mathematics, Siberian Branch of the Russian Academy of Sciences,Novosibirsk 630090, Russia aut Mikhailov G. A. Institute of Computational Mathematics, Siberian Branch of the Russian Academy of Sciences,Novosibirsk 630090, Russia aut Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 19/5(2004-10-01), 433-448 0927-6467 19:5<433 2004 19 rnam https://doi.org/10.1515/1569398042395989 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569398042395989 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lukinov V. L. Institute of Computational Mathematics, Siberian Branch of the Russian Academy of Sciences,Novosibirsk 630090, Russia aut NATIONALLICENCE 700 1- Mikhailov G. A. Institute of Computational Mathematics, Siberian Branch of the Russian Academy of Sciences,Novosibirsk 630090, Russia aut NATIONALLICENCE 773 0- Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 19/5(2004-10-01), 433-448 0927-6467 19:5<433 2004 19 rnam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter