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Russian Universities Reports. Mathematics, 2021, Volume 26, Issue 133, Pages 26–34 (Mi vtamu213)  

This article is cited in 1 scientific paper (total in 1 paper)

Scientific articles

On application of the $i$-smooth analysis methodology to elaboration of numerical methods for solving functional differential equations

A. V. Kim

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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Abstract: The article discusses a number of aspects of the application of $i$-smooth analysis in the development of numerical methods for solving functional differential equations (FDE). The principle of separating finite- and infinite-dimensional components in the structure of numerical schemes for FDE is demonstrated with concrete examples, as well as the usage of different types of prehistory interpolation, those by Lagrange and Hermite. A general approach to constructing Runge–Kutta-like numerical methods for nonlinear neutral differential equations is presented. Convergence conditions are obtained and the order of convergence of such methods is established.
Keywords: functional differential equations; numerical methods; $i$-smooth analysis; systems with delays.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00352
The work is partially supported by the Russian Foundation for Basic Research (project no. 20-01-00352_а).
Document Type: Article
UDC: 517.988.8+517.929
Language: Russian
Citation: A. V. Kim, “On application of the $i$-smooth analysis methodology to elaboration of numerical methods for solving functional differential equations”, Russian Universities Reports. Mathematics, 26:133 (2021), 26–34
Citation in format AMSBIB
\Bibitem{Kim21}
\by A.~V.~Kim
\paper On application of the $i$-smooth analysis methodology to~elaboration of numerical methods for solving functional~differential~equations
\jour Russian Universities Reports. Mathematics
\yr 2021
\vol 26
\issue 133
\pages 26--34
\mathnet{http://mi.mathnet.ru/vtamu213}
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  • https://www.mathnet.ru/eng/vtamu/v26/i133/p26
  • This publication is cited in the following 1 articles:
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