The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

Mamuli Zakradze, Zaza Tabagari, Nana Koblishvili, Tinatin Davitashvili, Jose Maria Sanchez and Francisco Criado-Aldeanueva ()
Additional contact information
Mamuli Zakradze: Department of Computational Methods, Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, 0186 Tbilisi, Georgia
Zaza Tabagari: Department of Computational Methods, Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, 0186 Tbilisi, Georgia
Nana Koblishvili: Department of Computational Methods, Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, 0186 Tbilisi, Georgia
Tinatin Davitashvili: Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, 0179 Tbilisi, Georgia
Jose Maria Sanchez: Deparment of Didactic of Mathematics, Faculty of Education, Malaga University, 29071 Malaga, Spain
Francisco Criado-Aldeanueva: Department of Applied Physics, II, Polytechnic School, Malaga University, 29071 Malaga, Spain

Mathematics, 2023, vol. 11, issue 3, 1-12

Abstract: 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.

Keywords: external Dirichlet generalized harmonic problem; probabilistic solution; Wiener process; computer simulation; sphere (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/3/539/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/3/539/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:539-:d:1041256

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().