Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 3, Pages 495–508 (Mi zvmmf690)  
Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation

V. L. Lukinov, G. A. Mikhailov

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent'eva 6, Novosibirsk, 630090, Russia
Full-text PDF (1512 kB)
References:
PDF
HTML
Abstract: Results of solving the first boundary value problem for a polyharmonic equation are presented. The technique is based on the probabilistic representation of the solution of this problem constructed by the authors. Such a solution is shown to be a parametric derivative of the solution of a special Dirichlet problem for the Helmholtz equation. Based on this fact, new “walk-by-spheres” algorithms for a polyharmonic equation are developed. This made it possible to construct an algorithm implementing the Monte Carlo method for estimating the covariance function of the solution of a biharmonic equation with random functional parameters.
Key words: polyharmonic equation, Monte Carlo method, Dirichlet problem, “walk-by-spheres” algorithm, random parameters.
Received: 14.09.2004
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: V. L. Lukinov, G. A. Mikhailov, “Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation”, Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005), 495–508; Comput. Math. Math. Phys., 45:3 (2005), 476–489
Citation in format AMSBIB
\Bibitem{LukMik05}
\by V.~L.~Lukinov, G.~A.~Mikhailov
\paper Monte Carlo methods for solving the first boundary value problem for a~polyharmonic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 3
\pages 495--508
\mathnet{http://mi.mathnet.ru/zvmmf690}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2161490}
\zmath{https://zbmath.org/?q=an:1114.65002}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 3
\pages 476--489
Linking options:
  • https://www.mathnet.ru/eng/zvmmf690
  • https://www.mathnet.ru/eng/zvmmf/v45/i3/p495
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025