# Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

## Abstract

A method based on the Taylor formula for the approximate solution of the Cauchy problem for the ordinary differential equation is studied. The problem of estimating the accuracy of the approximate solution generated by this method is considered, and an estimate of high accuracy is obtained for the difference of the exact and approximate solution. Here, different from the known values, an exact expression for the estimation coefficient is found.

## First Page

120

## Last Page

131

## References

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7. Azamov A.A., Abdullaev A.X., Tilavov A.M. On the derivation of an inequality for estimating the accuracy of an approximate solution to the initial value problem. Bulletin of the Institute of Mathematics, Vol. 5, pp. 105-111 (2022).

8. Abdullaev A.X., Azamov A.A., Ruziboev M.B. An explicit estimate for approximate solutions based on the Taylor formula. Ural mathematical journal. (submitted)

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## Recommended Citation

Abdullaev, Abdugani
(2023)
"Error estimation for the third-order accuracy approximate solution of the Cauchy problem by the Taylor formula,"
*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*: Vol. 6:
Iss.
3, Article 1.

DOI: https://doi.org/10.56017/2181-1318.1252