On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs

Authors

  • A. Abdullaev V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences Author
  • A. Azamov Author
  • M. Ruziboev Author
  • A. Tilavov Author

DOI:

https://doi.org/10.29229/uzmj.2026-2-1

Keywords:

Dynamical system, Cauchy problem, approximate solution, Taylor formula, Gronwall’s lemma, solution accuracy, accuracy level, error estimation.

Abstract

In this work, we obtain explicit estimates for the accuracy of an approximation solution scheme for ODEs. The scheme is of the fourth order and based on the Taylor formula. Here we derive estimates with explicit constants, which are expressed by the derivatives of the right-hand side.

Downloads

Published

2026-06-12

Issue

Vol. 70 No. 2 (2026): Uzbek Mathematical Journal

Section

Published

How to Cite

On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs. (2026). Uzbek Mathematical Journal, 70(2), 5-14. https://doi.org/10.29229/uzmj.2026-2-1