Abstract:
In this paper, we consider a third-order explicit scheme based on Taylor's formula to obtain an approximate solution for the Cauchy problem of systems of ODEs. We prove an estimate for the accuracy of the approximate solution with an explicit constant that depends only on the right-hand side of the equation and the domain of the solution.
Keywords:Dynamical systems, Cauchy problem, Approximate solution, Taylor formula, Accuracy of approximate solution, Level of accuracy, Error term
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Abdugani Kh. Abdullaev, Abdulla A. Azamov, Marks B. Ruziboev, “An explicit estimate for approximate solutions of ODEs based on the Taylor formula”, Ural Math. J., 10:1 (2024), 18–27
\Bibitem{AbdAzaRuz24}
\by Abdugani~Kh.~Abdullaev, Abdulla~A.~Azamov, Marks~B.~Ruziboev
\paper An explicit estimate for approximate solutions of ODEs based on the Taylor formula
\jour Ural Math. J.
\yr 2024
\vol 10
\issue 1
\pages 18--27
\mathnet{http://mi.mathnet.ru/umj217}
\crossref{https://doi.org/10.15826/umj.2024.1.002}
\elib{https://elibrary.ru/item.asp?id=68586401}
\edn{https://elibrary.ru/GTYJOG}
Citation in format AMSBIB
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