O‘zbekiston matematika jurnali Том 70 № 2 (2026) · с. 5-14

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

Abdullaev, Abdugani, Azamov, Abdulla, Ruziboev, Marks, Tilavov, Asliddin

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Аннотация

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.

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

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APA 7 
Abdullaev, Abdugani, Azamov, Abdulla, Ruziboev, Marks & Tilavov, Asliddin (2026). On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs. O‘zbekiston matematika jurnali, 70(2), 5-14.
GOST R 7.0.5 
Abdullaev, Abdugani, Azamov, Abdulla, Ruziboev, Marks, Tilavov, Asliddin On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs // O‘zbekiston matematika jurnali. 2026. Т. 70. № 2. С. 5-14.
BibTeX 
@article{abdugani2026,
  author  = {Abdullaev, Abdugani and Azamov, Abdulla and Ruziboev, Marks and Tilavov, Asliddin},
  title   = {On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2026},
  volume  = {70},
  number  = {2},
  pages   = {5-14}
}
RIS 
TY  - JOUR
AU  - Abdullaev, Abdugani
AU  - Azamov, Abdulla
AU  - Ruziboev, Marks
AU  - Tilavov, Asliddin
TI  - On the accuracy of approximate solution scheme based on the Taylor formula fora Cauchy problem for ODEs
JO  - O‘zbekiston matematika jurnali
PY  - 2026
VL  - 70
IS  - 2
SP  - 5
EP  - 14
ER  -