IKKI O’LCHOVLI SOHADA DIFFUZIYA JARAYONINI MATEMATIK MODELLASHTRISH
Keywords:
Kalit so‘zlar: diffuziya, ikki o‘lchovli model, matematik modellashtirish, qisman differensial tenglamalar, Fik qonuni, sonli usullar, analitik yechim, chegaraviy shartlar, ekologiya, materialshunoslik, biologiya, tibbiyot, kimyo texnologiyasi, issiqlik tenglamasi, Brown harakati, kompyuter simulyatsiyasi, sonli differensial usullar, sonli elementlar usuli, sonli hajmlar usuli, spektral usullar.Abstract
Annotatsiya: Ushbu maqolada ikki o‘lchovli sohada diffuziya jarayonini
matematik modellashtirish masalasi ko‘rib chiqiladi. Diffuziya — moddalar
konsentratsiyasining vaqt va makon bo‘yicha tarqalish jarayoni bo‘lib, uni matematik
tenglamalar yordamida ifodalash murakkab tizimlarni tahlil qilishda muhim
ahamiyatga ega. Tadqiqotda J. Crankning “The Mathematics of Diffusion” (Oxford
University Press, 1975) asarida bayon etilgan nazariy asoslar hamda reaksiya-diffuziya
tenglamalari bo‘yicha zamonaviy yondashuvlar qo‘llanildi. Maqolada ikki o‘lchovli
diffuziya tenglamasining analitik va sonli yechimlari, chegaraviy shartlarning ta’siri,
hamda kompyuter simulyatsiyalari orqali natijalarni vizualizatsiya qilish usullari
yoritiladi. Ushbu tadqiqot fizik, kimyoviy va biologik jarayonlarni chuqurroq
tushunishga xizmat qiladi va amaliy qo‘llanilish imkoniyatlarini kengaytiradi.
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