AN EXPLICIT ESTIMATE FOR APPROXIMATE SOLUTIONS OF ODES BASED ON THE TAYLOR FORMULA

AN EXPLICIT ESTIMATE FOR APPROXIMATE SOLUTIONS OF ODES BASED ON THE TAYLOR FORMULA

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...

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Bibliographic Details
Main Authors: Abdulla Kh. Abdullayev, Abdulla A. Azamov, Marks B. Ruziboev
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2024-07-01
Series:Ural Mathematical Journal
Subjects:
dynamical systems, cauchy problem, approximate solution, taylor formula, accuracy precision of an approximate solution, level of accuracy, error term
Online Access:https://umjuran.ru/index.php/umj/article/view/730
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Summary: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.
ISSN:2414-3952

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