The article studies the dynamics of derivatives up to the highest derivative of an ordinary differential equation of the fourth order with a small parameter at the highest derivative. The solution of the differential problem is sought in the form of a series in Chebyshev polynomials of the first kind with unknown expansion coefficients. Substituting these series into the differential problem, we obtain a system of algebraic equations for finding the unknown expansion coefficients. Using these coefficients, we calculate the solution to the problem and its derivatives. To illustrate the high accuracy of the applied method, we use the method of trial functions. The essence of the method of trial functions is as follows. A certain function is selected, it can be chosen arbitrarily. Substituting it into the main differential equation, we find the right-hand side and satisfy the corresponding boundary conditions. The resulting problem is solved by the spectral method and the approximate solution is compared with the known trial function and its derivatives for different values of the small parameter and the approximating Chebyshev polynomials.
| Mualliflar | Normurodov, Ch.B., Juraeva, N.T., Normatova, M.M., Нормуродов, Ч.Б., Джураева, Н.Т., Норматова, М.М. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-09-20 |
| Son | 4 |
| Betlar | 97-109 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.4_68.2025.03 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.4_68.2025.03 · Maqolaning asl sahifasi
Chebyshev polynomials, small parameter, high accuracy, полиномы Чебышева, малый параметр, высокая точность
| APA | Normurodov, Ch.B., Juraeva, N.T., Normatova, M.M., Нормуродов, Ч.Б., Джураева, Н.Т., & Норматова, М.М. (2025). Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative. Ҳисоблаш ва амалий математика муаммолари, (4), 97-109. https://doi.org/10.71310/pcam.4_68.2025.03 |
|---|---|
| GOST (OAK) | Normurodov, Ch.B. va b. Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4. – P. 97-109. – DOI: 10.71310/pcam.4_68.2025.03. |
| MLA | Normurodov, Ch.B., Juraeva, N.T., Normatova, M.M., Нормуродов, Ч.Б., Джураева, Н.Т., and Норматова, М.М. “Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative.” Ҳисоблаш ва амалий математика муаммолари, (4), 97-109, 2025. https://doi.org/10.71310/pcam.4_68.2025.03 |
| Chicago | Normurodov, Ch.B., Juraeva, N.T., Normatova, M.M., Нормуродов, Ч.Б., Джураева, Н.Т., and Норматова, М.М. “Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative.” Ҳисоблаш ва амалий математика муаммолари, (4), 97-109 (2025). https://doi.org/10.71310/pcam.4_68.2025.03 |
| Harvard | Normurodov, Ch.B., Juraeva, N.T., Normatova, M.M., Нормуродов, Ч.Б., Джураева, Н.Т., and Норматова, М.М (2025) ‘Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative’, Ҳисоблаш ва амалий математика муаммолари, (4), 97-109. https://doi.org/10.71310/pcam.4_68.2025.03 |
| BibTeX | @article{normurodovchb2025,
title = {Study of the Dynamics of Derivatives of a Fourth-Order Differential Equation with a Small Parameter at the Highest Derivative},
author = {Normurodov, Ch.B. and Juraeva, N.T. and Normatova, M.M. and Нормуродов, Ч.Б. and Джураева, Н.Т. and Норматова, М.М.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4},
pages = {97-109},
doi = {10.71310/pcam.4_68.2025.03},
url = {https://doi.org/10.71310/pcam.4_68.2025.03}
} |
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