Geodesic
An explicit estimate for approximate solutions of ODEs based on the Taylor formula
Ural mathematical journal, Tome 10 (2024) no. 1, pp. 18-27

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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
Mots-clés : Error term 
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     title = {An explicit estimate for approximate solutions of {ODEs} based on the {Taylor} formula},
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Abdugani Kh. Abdullaev; Abdulla A. Azamov; Marks B. Ruziboev. An explicit estimate for approximate solutions of ODEs based on the Taylor formula. Ural mathematical journal, Tome 10 (2024) no. 1, pp. 18-27. http://geodesic.mathdoc.fr/item/UMJ_2024_10_1_a1/