INTEGRAL TENGLAMALARNING ZAMONAVIY YECHIM USULLARI

Muxlisa Xurramova

doi:10.5281/zenodo.20379994

Mualliflar

Xurramova Muxlisa Kattaqo‘rg‘on Davlat Pedagogika instituti Aniq va tabiiy fanlar fakulteti Matematika yo'nalishi m_25_01 guruh talabasi

Annotatsiya

Ushbu maqolada integral tenglamalarning nazariy asoslari va ularni yechishning zamonaviy usullari tahlil qilinadi. Integral tenglamalar matematika, fizika, muhandislik, iqtisodiyot va biologiyada murakkab jarayonlarni modellashtirishda keng qo‘llaniladi. Tadqiqotda Fredholm va Volterra tipidagi integral tenglamalar, shuningdek ularni yechishda qo‘llaniladigan Nyström, kollokatsiya, Galerkin, kvadratura va wavelet usullari ko‘rib chiqilgan. Sun’iy intellekt va mashinaviy o‘qitish asosidagi yangi yondashuvlarning imkoniyatlari ham baholangan. Tadqiqot natijalari integral tenglamalarni yechishda zamonaviy sonli usullar yuqori aniqlik, hisoblash tezligi va amaliy samaradorlikni ta’minlashini ko‘rsatadi.

Kalit soʻzlar:

integral tenglama Fredholm tenglamasi Volterra tenglamasi Nyström usuli Galerkin usuli kollokatsiya usuli kvadratura usuli wavelet usuli mashinaviy o‘qitish.

Iqtiboslar

Linear Integral Equations. Boston: Birkhäuser, 1997. B. 15–42, 85–118.

A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. Philadelphia: Society for Industrial and Applied Mathematics, 1976. B. 23–67.

Linear Integral Equations. New York: Springer, 2014. B. 41–96, 183–245.

Analytical and Numerical Methods for Volterra Equations. Oxford: Oxford University Press, 2004. B. 52–134.

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Integral Equations. New York: Dover Publications, 1985. B. 17–93.

Introduction to Integral Equations with Applications. Hoboken: John Wiley & Sons, 1999. B. 35–112.

INTEGRAL TENGLAMALARNING ZAMONAVIY YECHIM USULLARI

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