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


Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 8, Pages 1498–1505 (Mi zvmmf617)  

This article is cited in 5 scientific papers (total in 5 papers)

Meshless method based on radial basis functions

A. I. Tolstykh, D. A. Shirobokov

Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: A numerical method for partial differential equations based on radial basis functions (RBF) is described. In the method, spatial derivatives are approximated using RBF interpolants with local supports analogous to stencils used in finite-difference methods. The numerical results presented for various elasticity problems reveal that the method provides good accuracy and convergence. The method is also applied to problems with non-self-adjoint operators (like those in the Navier–Stokes equations).

Key words: meshless numerical solver, method of radial basis functions, finite-difference methods in fluid dynamics.

Full text: PDF file (1228 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2005, 45:8, 1447–1454

Bibliographic databases:
UDC: 519.63
Received: 26.11.2004

Citation: A. I. Tolstykh, D. A. Shirobokov, “Meshless method based on radial basis functions”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1498–1505; Comput. Math. Math. Phys., 45:8 (2005), 1447–1454

Citation in format AMSBIB
\Bibitem{TolShi05}
\by A.~I.~Tolstykh, D.~A.~Shirobokov
\paper Meshless method based on radial basis functions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 8
\pages 1498--1505
\mathnet{http://mi.mathnet.ru/zvmmf617}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191859}
\zmath{https://zbmath.org/?q=an:1084.76059}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 8
\pages 1447--1454


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf617
  • http://mi.mathnet.ru/eng/zvmmf/v45/i8/p1498

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gorbachenko V.I., Artyukhina E.V., “Issledovanie gradientnykh algoritmov obucheniya vesov radialnobazisnykh neironnykh setei dlya resheniya kraevykh zadach matematicheskoi fiziki”, Izv. Penzenskogo gos. ped. un-ta im. V. G. Belinskogo, 2009, no. 17, 134–143
    2. Matveeva N.O., Artyukhina E.V., “Reshenie uravneniya Puassona na massivnoparallelnom graficheskom protsessore s ispolzovaniem neirosetevoi optimizatsii”, Izv. Penzenskogo gos. pedagogich. un-ta im. V. G. Belinskogo, 2010, no. 22, 189–195  elib
    3. Gorbachenko V.I., Matveeva N.O., Gurin E.I., “Rasparallelivanie neirosetevogo algoritma resheniya kraevykh zadach matematicheskoi fiziki na mnogoyadernykh protsessorakh nvidia”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Tekhnicheskie nauki, 2011, no. 4, 57–65  elib
    4. V. I. Gorbachenko, M. V. Zhukov, “Solving boundary value problems of mathematical physics using radial basis function networks”, Comput. Math. Math. Phys., 57:1 (2017), 145–155  mathnet  crossref  crossref  isi  elib
    5. L. N. Elisov, V. I. Gorbachenko, M. V. Zhukov, “Learning radial basis function networks with the trust region method for boundary problems”, Autom. Remote Control, 79:9 (2018), 1621–1629  mathnet  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:791
    Full text:402
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021