IKKI O‘LCHOVLI PARABOLIK TENGLAMANI AYIRMALI SXEMA YORDAMIDA SONLI YECHISH VA DASTURIY REALIZATSIYASI
DOI:
https://doi.org/10.5281/zenodo.20352565Keywords:
parabolik tenglama, issiqlik tenglamasi, ayirmali sxema, explicit sxema, sonli usullar, MATLAB, Python, modellashtirish.Abstract
Mazkur maqolada ikki o‘lchovli konveksiya-diffuziya tenglamasini sonli usullar yordamida yechish masalasi ko‘rib chiqilgan. Tenglama diffuziya hadlari bilan birga ∂u/∂x ko‘rinishidagi konveksiya (adveksiya) hadini o‘z ichiga oladi, bu esa masalani klassik issiqlik tenglamasiga nisbatan murakkablroq qiladi. Tadqiqotda aniq (explicit) ayirmali sxema asosida tenglama diskretlashtirildi va Python hamda MATLAB muhitlarida dasturiy realizatsiya qilindi. Olingan natijalar grafik ko‘rinishda tahlil qilinib, usulning samaradorligi ko‘rsatildi.References
Samarskiy A.A. “The Theory of Difference Schemes”. - Moscow: Nauka, 1983.
Morton K., Mayers D. “Numerical Solution of Partial Differential Equations”. - Cambridge University Press, 2005.
Smith G.D. “Numerical Solution of Partial Differential Equations: Finite Difference Methods”. - Oxford University Press, 1985.
Ames W.F. “Numerical Methods for Partial Differential Equations”. - Academic Press, 1992.
LeVeque R.J. “Finite Difference Methods for Ordinary and Partial Differential Equations”. - SIAM, 2007.
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2026-05-23
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Usmonova, Z., & Ismoilov, A. (2026). IKKI O‘LCHOVLI PARABOLIK TENGLAMANI AYIRMALI SXEMA YORDAMIDA SONLI YECHISH VA DASTURIY REALIZATSIYASI. Science and Innovation, 4(44), 143-150. https://doi.org/10.5281/zenodo.20352565
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