Ikkinchi tartibli differensial tenglamalar uchun lokal chegaraviy masalalar: nazariya va tatbiqlari
DOI:
https://doi.org/10.5281/zenodo.19653294Ключевые слова:
differensial tenglama, lokal chegaraviy shart, Grin funksiyasi, chekli farqlar usuli, yechimning yagonaligi, elliptik operator, Shturm–Liuvill masalasiАннотация
Ikkinchi tartibli chiziqli differensial tenglamalar uchun lokal chegaraviy masalalarning nazariy asoslari va
amaliy tatbiqlari o‘rganiladi. Yechimning mavjudligi va yagonaligiga oid teoremalar isbotlanadi, Grin funksiyasi yordamida
yechimni qurishning analitik usuli bayon etiladi. Chekli farqlar sxemasi asosida sonli algoritm ishlab chiqilib, uning yaqinlashish
tartibi ko‘rsatiladi. Issiqlik o‘tkazuvchanlik va elastiklik nazariyasidan olingan amaliy misollar orqali usulning samaradorligi
tasdiqlanadi.
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