@article{Zakradze2025, 
author = {Mamuli Zakradze and Zaza Tabagari and Nana Koblishvili and Tinatin Davitashvili and José-María Sánchez-Sáez and Francisco Criado-Aldeanueva},
title = {The numerical solution of the Dirichlet generalized and classical harmonic problems for irregular    n-sided pyramidal domains by the method of probabilistic solutions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {17657-17671},
keywords = {Dirichlet generalized and classical harmonic problems, method of probabilistic solution, Wiener process, pyramidal domain},
url = {https://www.sciopen.com/article/10.3934/math.2025789},
doi = {10.3934/math.2025789},
abstract = {This paper describes the application of the method of probabilistic solutions (MPS) to numerically solve the Dirichlet generalized and classical harmonic problems for irregular    n-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.}
}