Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method

Жумаев, З.З., Jumaev, Z.Z.

Ҳисоблаш ва амалий математика муаммолари · 2026-yil

Annotatsiya

This study presents an efficient method for approximating the solutions of a certain class of first-order differential equations with variable coefficients. The approach constructs an auxiliary differential equation that combines the Runge-Kutta method with a piecewise constant argument, derived from the original initial value problem and parameterized by a positive integer ????. It is shown that, for sufficiently large ????, this auxiliary equation has a unique piecewise-smooth solution that approximates the considered initial value problem. Error estimates for the residual are derived to quantify the accuracy and to illustrate the influence of ????. The numerical results show that the method achieves higher accuracy with fewer computational steps than the classical Runge-Kutta and related schemes, and the framework extends to a broader class of nonlinear equations.

Maqola ma’lumotlari
MualliflarЖумаев, З.З., Jumaev, Z.Z.
JurnalҲисоблаш ва амалий математика муаммолари
NashriyotТошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази
ISSN2181-8460, 2181-046X
Nashr sanasi2026-07-02
Son3
Betlar153-163
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.71310/pcam.3_73.2026.11
Indeksga qo‘shilgan2026-08-27

DOI: 10.71310/pcam.3_73.2026.11 · Maqolaning asl sahifasi

Kalit so‘zlar

initial value problem, piecewise constant argument, approximated solution, Runge-Kutta method, absolute error, задача с начальными условиями, кусочно-постоянный аргумент, приближённое решение, метод Рунге–Кутты, абсолютная погрешность

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAЖумаев, З.З., & Jumaev, Z.Z. (2026). Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method. Ҳисоблаш ва амалий математика муаммолари, (3), 153-163. https://doi.org/10.71310/pcam.3_73.2026.11
GOST (OAK)Жумаев, З.З., Jumaev, Z.Z. Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 3. – P. 153-163. – DOI: 10.71310/pcam.3_73.2026.11.
MLAЖумаев, З.З., and Jumaev, Z.Z. “Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method.” Ҳисоблаш ва амалий математика муаммолари, (3), 153-163, 2026. https://doi.org/10.71310/pcam.3_73.2026.11
ChicagoЖумаев, З.З., and Jumaev, Z.Z. “Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method.” Ҳисоблаш ва амалий математика муаммолари, (3), 153-163 (2026). https://doi.org/10.71310/pcam.3_73.2026.11
HarvardЖумаев, З.З., and Jumaev, Z.Z (2026) ‘Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method’, Ҳисоблаш ва амалий математика муаммолари, (3), 153-163. https://doi.org/10.71310/pcam.3_73.2026.11
BibTeX
@article{article2026,
  title = {Approximate Solution of Initial Value Problems for First-Order Differential Equations using a Combined Runge-Kutta And Piecewise Constant Argument Method},
  author = {Жумаев, З.З. and Jumaev, Z.Z.},
  journal = {Ҳисоблаш ва амалий математика муаммолари},
  year = {2026},
  number = {3},
  pages = {153-163},
  doi = {10.71310/pcam.3_73.2026.11},
  url = {https://doi.org/10.71310/pcam.3_73.2026.11}
}

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