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Maqolada murakkab dinamik jarayonlarni matematik modellashtirish, oddiy differensial tenglamalar tizimlari orqali ifodalash va ularni sonli usullar yordamida tadqiq etish masalalari ko‘rib chiqildi. Nazariy qismda model qurish, diskretlash, verifikatsiya, validatsiya, qadam tanlash, barqarorlik va hisoblash xatolari o‘rtasidagi bog‘lanish tahlil qilindi. Amaliy tajriba sifatida Lorenzning uch o‘lchovli nolinear tizimi tanlanib, Euler, klassik to‘rtinchi tartibli Runge–Kutta, adaptiv RK45 va DOP853 usullari bilan yechildi. Hisoblashlar Euler usulining kichik qadamda ham yuqori global xatoga ega ekanini, RK4 esa xuddi shu qadamda ancha aniq natija berishini ko‘rsatdi. Boshlang‘ich shartni 10⁻⁸ miqdorga o‘zgartirish uzoq vaqt oralig‘ida trayektoriyalarning sezilarli ajralishiga olib keldi. Bu holat xaotik tizimlarda yuqori tartibli algoritmning o‘zi yetarli emasligini, natijani talqin qilishda model sezgirligi va prognoz gorizontini ham hisobga olish zarurligini ko‘rsatadi.References
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