Lineynye Differentsial'nye Uravneniya S Obobshchennymi Koeffitsientami : v algebre mnemofunktsiy

Dannaya kniga posvyashchena issledovaniyu resheniy zadachi Koshi dlya lineynykh differentsial'nykh uravneniy vtorogo poryadka s obobshchennymi koeffitsientami. Takie uravneniya ne okhvatyvayutsya klassicheskoy teoriey differentsial'nykh uravneniy, poskol'ku mogut soderzhat' proizvedeniya obobshchennykh funktsiy. Izvestno neskol'ko podkhodov (P.Antosik, F.Atkinson, P.S.Das, S.Zh.Deo, S.T.Zavalishchin, Ya.Kurtsveyl', Ya.Ligeza, Ya.Mikusinskiy, S.Zh.Pandit, A.N.Sesekin, R.Sikorskiy, R.R.Sharma) dlya opredeleniya resheniy differentsial'nykh uravneniy s obobshchennymi koeffitsientami, no edinogo obshcheprinyatogo opredeleniya poka net. V dannoy knige razvivaetsya metod algebr mnemofunktsiy dlya opredeleniya proizvedeniya obobshchennykh funktsiy. Preimushchestvo dannogo metoda sostoit v tom, chto on pozvolyaet s edinykh pozitsiy okhvatit' analogichnye rezul'taty i mozhet byt' effektivno ispol'zovan pri chislennom modelirovanii resheniy zadach podobnogo tipa. V knige dokazany teoremy sushchestvovaniya i edinstvennosti assotsiirovannykh resheniy, na osnove apparata vvedennykh assotsiirovannykh fundamental'nykh matrits, assotsiirovannykh funktsiy Koshi, assotsiirovannykh vronskianov postroena obshchaya teoriya lineynykh differentsial'nykh uravneniy s obobshchennymi koeffitsientami.