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Russian Universities Reports. Mathematics, 2021, Volume 26, Issue 133, Pages 26–34
(Mi vtamu213)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/vtamu213 https://www.mathnet.ru/eng/vtamu/v26/i133/p26
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Statistics & downloads: |
Abstract page: | 109 | Full-text PDF : | 49 | References: | 19 |
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