Vol. 3 No. 9 (2026), Articles
Vol. 3 No. 9 (2026)

ODDIY DIFFERENSIAL TENGLAMALAR SISTEMASINI KOSHI MASALASI BO‘YICHA SONLI YECHISH

Articles
Published 2026-01-17
Abdurahmonov Asomiddin
Termiz Davlat Universiteti Magistratura bo‘limi, Amaliy matematika yo‘nalishi M-124 guruh magistranti:
PDF

Keywords

Koshi masalasi, oddiy differensial tenglama, sonli metodlar, Eyler metodi, Runge–Kutta metodi, ayirmali sxema, yaqinlashish, approksimatsiya xatoligi, ko‘p qadamli metodlar.

Abstract

Ushbu ishda oddiy differensial tenglamalar uchun Koshi masalasini yechishning asosiy sonli metodlari ko‘rib chiqilgan. Koshi masalasining qo‘yilishi, yechimning mavjudligi va birdan-birligi shartlari bayon etilgan. Sonli yechim usullari sifatida Eyler metodi, simmetrik ayirmali sxema, ikkinchi tartibli Runge–Kutta metodlari hamda ko‘p qadamli ayirmali metodlar tahlil qilingan. Metodlarning approksimatsiya xatoligi va yaqinlashish xususiyatlari o‘rganilgan. Olingan natijalar sonli metodlarning aniqligi va qo‘llanilish sohalarini baholash imkonini beradi.

PDF

References

1. Samarsky, A.A. Numerical Methods for Ordinary Differential Equations. Moscow: Nauka, 2001.

2. Butkovskiy, A.G. Differential Equations: Theory and Applications. Moscow: Fizmatlit, 2005.

3. Ascher, U.M., Petzold, L.R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM, 1998.

4. Hairer, E., Nørsett, S.P., Wanner, G. Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, 1993.

5. Iserles, A. A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press, 2009.

6. Butcher, J.C. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, 2016.

7. Burden, R.L., Faires, J.D. Numerical Analysis. Brooks/Cole, 2011.