Abstract
Ushbu tadqiqot ishida hisoblash matematikasining fundamental muammolaridan biri bo‘lgan nochiziqli tenglamalarni yechishning taqribiy usullari batafsil tahlil qilinadi. Tadqiqot doirasida biseksiya, Nyutonning klassik va soddalashgan usullari, shuningdek, kesuvchilar (vatarlar) usullarining nazariy asoslari, yaqinlashish shartlari va xatoliklar tartibi o‘rganilgan. Maqolada har bir usulning algoritmik samaradorligi turli murakkablikdagi transsendent tenglamalar misolida qiyoslanadi. Tadqiqot natijalari Python dasturlash tili yordamida olingan eksperimental ma’lumotlar, grafiklar va iteratsiyalar dinamikasi bilan boyitilgan. Olingan natijalar muhandislik va ilmiy hisoblashlarda optimal metodni tanlash mezonlarini belgilashga xizmat qiladi.
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