Email this article On application of the i-smooth analysis methodology to elaboration of numerical methods for solving functional differential equations
- Authors: Kim A.V.1
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Affiliations:
- N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
- Issue: Vol 26, No 133 (2021)
- Pages: 26-34
- Section: Original articles
- URL: https://bakhtiniada.ru/2686-9667/article/view/296363
- ID: 296363
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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.
About the authors
Arkadii V. Kim
N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Author for correspondence.
Email: avkim@imm.uran.ru
Doctor of Physics and Mathematics, Senior Scientific Researcher
Russian Federation, 16 S. Kovalevskaya St., Yekaterinburg 620108, Russian FederationReferences
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