This paper investigates the qualitative properties of self-similar solutions of a nonlinear cross-diffusion system with nonlinear boundary conditions and a source. A self-similar solution of the cross-diffusion problem is constructed. In the case of global solvability, the leading term of the asymptotics of self-similar solutions of the cross-diffusion problem with a source is obtained. When numerically solving nonlinear problems using iterative methods, it is crucial to choose a suitable initial approximation that preserves the nonlinear properties. Computational experiments have shown the rapid convergence of the iterative process to the exact solution, due to the choice of a suitable initial approximation. The use of asymptotic formulas as initial approximations in iterative methods significantly increases the chances of rapid convergence of the algorithm and improves the accuracy of the numerical results obtained.
| Mualliflar | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., Урунбаев, Ж.Э. |
|---|---|
| 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 | 2024-07-19 |
| Son | 3 |
| Betlar | 114-121 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-08-27 |
asymptotics, cross-diffusion, nonlinear system, self-similar solution, iteration, кросс диффузии, асимптотика, нелинейные граничные условия, начальные приближения
| APA | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., & Урунбаев, Ж.Э. (2024). Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source. Ҳисоблаш ва амалий математика муаммолари, (3), 114-121. https://journals.airi.uz/index.php/pvpm/article/view/27 |
|---|---|
| GOST (OAK) | Rakhmonov, Z.R. va b. Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 3. – P. 114-121. |
| MLA | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., and Урунбаев, Ж.Э. “Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source.” Ҳисоблаш ва амалий математика муаммолари, (3), 114-121, 2024. https://journals.airi.uz/index.php/pvpm/article/view/27 |
| Chicago | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., and Урунбаев, Ж.Э. “Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source.” Ҳисоблаш ва амалий математика муаммолари, (3), 114-121 (2024). https://journals.airi.uz/index.php/pvpm/article/view/27 |
| Harvard | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., and Урунбаев, Ж.Э (2024) ‘Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source’, Ҳисоблаш ва амалий математика муаммолари, (3), 114-121. https://journals.airi.uz/index.php/pvpm/article/view/27 |
| BibTeX | @article{rakhmonovzr2024,
title = {Numerical solution of the cross-diffusion problem with nonlinear boundary conditions and source},
author = {Rakhmonov, Z.R. and Urunbaev, J.E. and Рахмонов, З.Р. and Урунбаев, Ж.Э.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {3},
pages = {114-121},
url = {https://journals.airi.uz/index.php/pvpm/article/view/27}
} |
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