RT Journal Article
T1 The numerical solution of the Dirichlet generalized and classical harmonic problems for irregular n-sided pyramidal domains by the method of probabilistic solutions
A1 Zakradze, Mamuli
A1 Tabagari, Zaza
A1 Koblishvili, Nana
A1 Davitashvili, Tinatin
A1 Sánchez-Sáez, José María
A1 Criado-Aldeanueva, Francisco
K1 Wiener, Integrales de
K1 Probabilidades
K1 Dirichlet, Problema de
AB This paper describes the application of the method of probabilistic solutions (MPS) to numerically solve the Dirichlet generalized and classical harmonic problems for irregular -sided pyramidal domains. Here, "generalized" means that the boundary function has a finite number of first-kind discontinuity curves, with the pyramid edges acting as these curves. The pyramid's base is a convex polygon, and its vertex projection lies within the base. The proposed algorithm for solving boundary problems numerically includes the following steps: a) applying MPS, which relies on computer modeling of the Wiener process; b) determining the intersection point between the simulated Wiener process path and the pyramid surface; c) developing a code for numerical implementation and verifying the accuracy of the results; d) calculating the desired function's value at any chosen point. Two examples are provided for illustration, and the results of the numerical experiments are presented and discussed.
PB AIMS Press
YR 2025
FD 2025-08
LK https://hdl.handle.net/10630/39708
UL https://hdl.handle.net/10630/39708
LA eng
NO Zakradze, M., Tabagari, Z., Koblishvili, N., Davitashvili, T., Sánchez-Sáez, J.-M., & Criado-Aldeanueva, F. (2025). The numerical solution of the Dirichlet generalized and classical harmonic problems for irregular n-sided pyramidal domains by the method of probabilistic solutions. AIMS Mathematics, 10(8), 17657-17671. https://doi.org/10.3934/math.2025789
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026