An approximation algorithm for quadratic dynamic systems based on N. Chomsky’s grammar for Taylor’s formula

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 th...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2016-07, Vol.293 (Suppl 1), p.17-21
Main Authors: Azamov, A. A., Bekimov, M. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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. The algorithm is based on N. Chomsky’s generative grammar for the language of terms of Taylor’s formula.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543816050023