Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




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

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 327, Pages 79–86
DOI: https://doi.org/10.4213/tm4424 (Mi tm4424) 		 
On the Newton–Kantorovich Scheme for Evolutionary Equations

Andrey V. Dymovabc, Sergei B. Kuksindace

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Peoples' Friendship University of Russia (RUDN University), Moscow, Russia
d Université Paris Cité & Sorbonne Université, CNRS, IMJ–PRG, Paris, France
e Institute for Financial Studies, Shandong University, Jinan, China
Full-text PDF (228 kB) First page
References:
PDF
HTML
DOI: https://doi.org/10.4213/tm4424
Abstract: We propose a constructive form of the Newton–Kantorovich method to obtain solutions for evolutionary equations with small nonlinearities. The construction is applicable to equations in non-Banach linear spaces. The paper presents only a sketch of the method, without specifying the norms involved and without giving necessary $\varepsilon $–$\delta $ details.
Keywords: evolutionary equations, Newton–Kantorovich scheme, KAM theory, approximate propagators.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1115
The research was supported by the Ministry of Science and Higher Education of the Russian Federation, megagrant no. 075-15-2022-1115.
Received: May 7, 2024
Revised: September 23, 2024
Accepted: September 25, 2024
Published: 12.03.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 327, Pages 70–77
DOI: https://doi.org/10.1134/S0081543824060063
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Andrey V. Dymov, Sergei B. Kuksin, “On the Newton–Kantorovich Scheme for Evolutionary Equations”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 79–86; Proc. Steklov Inst. Math., 327 (2024), 70–77
Citation in format AMSBIB
\Bibitem{DymKuk24}
\by Andrey~V.~Dymov, Sergei~B.~Kuksin
\paper On the Newton--Kantorovich Scheme for Evolutionary Equations
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 79--86
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4424}
\crossref{https://doi.org/10.4213/tm4424}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 70--77
\crossref{https://doi.org/10.1134/S0081543824060063}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001528334}
Linking options:
  • https://www.mathnet.ru/eng/tm4424
  • https://doi.org/10.4213/tm4424
  • https://www.mathnet.ru/eng/tm/v327/p79
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025