Симметрик t-гиперболик системалар учун чекли элементлар усули турғунлиги

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Asosiy mavzular

• “Симметрик t-гиперболик системалар учун чекли элементлар усули турғунлиги”: Mazkur dissertatsiya ishi jismoniy va matematik fanlar bo'yicha falsafa doktori (PhD) ilmiy darajasini olish uchun tayyorlangan. Unda simmetrik t-giperbolik sistema uchun aralash masalalarni chekli elementlar usuli yordamida yechishning noaniq ayirmali sxemalarini tuzish va ularning barqarorligini asoslash masalalari ko'rib chiqiladi. Tadqiqotda bir va ikki o'lchovli fazolarda ham doimiy, ham o'zgaruvchan koeffitsiyentli simmetrik t-giperbolik sistema uchun chekli elementlar usuli yordamida tuzilgan noaniq ayirmali sxemalarning barqarorligini ta'minlovchi shartlar topilgan va bu sxemalarni qo'llash uchun dasturiy ta'minot yaratilgan.
• “Устойчивость метода конечных элементов для симметрических t-гиперболических систем”: This abstract is prepared for obtaining the academic degree of Doctor of Philosophy (PhD) in Physical and Mathematical Sciences. It deals with the construction of implicit difference schemes for symmetric t-hyperbolic systems using the finite element method for solving mixed problems and proving their stability. The research has identified conditions ensuring the stability of implicit difference schemes constructed using the finite element method for symmetric t-hyperbolic systems in one- and two-dimensional spaces, both for constant and variable coefficients, and developed software for applying these schemes.