RT Journal Article
T1 The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution
A1 Zakradze, Mamuli
A1 Tabagari, Zaza
A1 Koblishvili, Nana
A1 Davitashvili, Tinatin
A1 Sánchez-Sáez, José María
A1 Criado-Aldeanueva, Francisco
K1 Simulación por ordenador
AB In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin’s theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.
PB IOAP-MDPI
YR 2023
FD 2023-01-19
LK https://hdl.handle.net/10630/26040
UL https://hdl.handle.net/10630/26040
LA eng
NO Zakradze M, Tabagari Z, Koblishvili N, Davitashvili T, Sanchez JM, Criado-Aldeanueva F. The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution. Mathematics. 2023; 11(3):539. https://doi.org/10.3390/math11030539
NO Partial funding for open access charge: Universidad de Málaga
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026