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-§. Eyler va Eyler-Koshi usullari
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| bet | 4/4 | | Sana | 25.05.2024 | | Hajmi | 103,92 Kb. | | #253917 |
Bog'liq KURS ISHI1.3-§. Eyler va Eyler-Koshi usullari.
Berilgan ushbu (1) formulada k=0 bo’lgan holda hisoblash jarayoni ,
(2)
formula bilan teshkil etiladi. Buni Eyler taklif qilgan, shuning uchun bunday hisoblash jarayoni Eyler me’todi deb yuritiladi. Eyler usulining quyidagicha modifikatsiyasi mavjud.
Avval quyidagi yaqinlashish
hisoblanadi, so’ng
(3)
formula yordamida nuqtadagi yechimning taqribiy qiymati topiladi.
Bu yerda
Ifoda Eyler usulining modifikatsiyasidir.
Eyler-Koshining modifikatsiyalangan metodi quyidagicha aniqlanadi.
Avval
hisoblanadi , so’ng nuqtadagi yechimning taqribiy qiymati
(4)
formula bilan aniqlanadi.
Bu yerda
Agar masalaning taqribiy yechimini
deb, uni quyidagi
(5)
iteratsion jarayon bilan berilgan aniqlik miqdorida topilsa (5) ifoda Eyler-Koshining iteratsion metodi deyiladi.
Xulosa qilib aytganda , ushbu Eyler va Eyler-Koshi usullari epidemiyaning SIR modelini sonli yechishda samarali usullardan biri hisoblanadi. Bu usullar ushbu jarayonlarning dasturini tuzishda ham qo’l keladi.
Dissertatsiya mavzusining tenglamasi quyidagicha:
(1)
t = 0 da boshlang’ich shartlar bilan:
(2)
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