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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 21–25 (Mi timm1167)  
An approximation algorithm for quadratic dynamic systems based on N. Chomsky's grammar for Taylor's formula

A. A. Azamov, M. A. Bekimov

Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek
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Abstract: Single-step methods for the approximate solution of the Cauchy problem for dynamic systems are discussed. It is shown that a numerical integration algorithm with a high degree of accuracy based on Taylor's formula can be proposed in the case of quadratic systems. An explicit estimate is given for the remainder term. The algorithm is based on N. Chomsky's generative grammar for the language of terms of Taylor's formula.
Keywords: dynamic system, quadratic system of equations, Cauchy problem, numerical solution, Taylor's formula, remainder term, error estimate, algorithm, context-free grammar.
Received: 16.02.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 17–21
DOI: https://doi.org/10.1134/S0081543816050023
Bibliographic databases:
Document Type: Article
UDC: 517.938, 519.624.3
Language: Russian
Citation: A. A. Azamov, M. A. Bekimov, “An approximation algorithm for quadratic dynamic systems based on N. Chomsky's grammar for Taylor's formula”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 21–25; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 17–21
Citation in format AMSBIB
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