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 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 159-166 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2026-2-19 |
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
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