This work introduces an efficient methodology for approximating solutions to first-order non-linear differential equations. The approach is based on formulating a differential equation with piecewise constant arguments associated with the parameters of the classical Runge-Kutta (RK) discrete equations depended on a positive integer parameter $n$. It is demonstrated that the constructed equation has a unique piecewise-smooth solution and for sufficiently large values of $n$, this solution approximating solution to the original problem. Numerical results are provided through examples, demonstrating the efficiency and high accuracy of the proposed method.
| Mualliflar | Muminov, M., Jumaev, Z. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 159-166 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-2-19 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-2-19 · Maqolaning asl sahifasi
Initial value problem, Differential equation with piecewise constant argument, Approximated solution, Runge-Kutta method, Absolute error
| APA | Muminov, M., & Jumaev, Z. (2026). Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations. O‘zbekiston matematika jurnali, 70(2), 159-166. https://doi.org/10.29229/uzmj.2026-2-19 |
|---|---|
| GOST (OAK) | Muminov, M., Jumaev, Z. Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 159-166. – DOI: 10.29229/uzmj.2026-2-19. |
| MLA | Muminov, M., and Jumaev, Z. “Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations.” O‘zbekiston matematika jurnali, 70(2), 159-166, 2026. https://doi.org/10.29229/uzmj.2026-2-19 |
| Chicago | Muminov, M., and Jumaev, Z. “Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations.” O‘zbekiston matematika jurnali, 70(2), 159-166 (2026). https://doi.org/10.29229/uzmj.2026-2-19 |
| Harvard | Muminov, M., and Jumaev, Z (2026) ‘Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations’, O‘zbekiston matematika jurnali, 70(2), 159-166. https://doi.org/10.29229/uzmj.2026-2-19 |
| BibTeX | @article{muminovm2026,
title = {Mixed piecewise constant argument and the Runge-Kutta method for numerically solving first-order differential equations},
author = {Muminov, M. and Jumaev, Z.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {2},
pages = {159-166},
doi = {10.29229/uzmj.2026-2-19},
url = {https://doi.org/10.29229/uzmj.2026-2-19}
} |
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