Riccati diferensiyel denklemi

Bu tez yedi bolumden olusmaktadir.Birinci bolum, giris kismina ayrilmistir.Ikinci bolumde, Riccati denklemi ve cozumu ile ilgili iliskiler verilmistir.Ucuncu bolumde, orijinal Riccati denklemi uzerinde durulmus ve elemanterfonksiyonlar cinsinden cozumlerini bulmak icin yontemler verilmistir.Dorduncu bolumde, sabit ve hareketli aykiri noktalardan bahsedilmis ve Riccatidenkleminin aykiriliklarinin karakteri hakkinda bilgi verilmistir.Besinci bolumde, Riccati denkleminin bazi ozel cozumlerini bulma yontemleriuzerinde durulmus ve R Riccati operatorunden bahsedilmistir.Altinci bolumde, genellestirilmis Riccati denklemi incelenmistir.Yedinci bolumde, Riccati denklemini degiskenlerine ayrilabilir denklemedonusturen iliskiler uzerinde durulmustur.abstractThis thesis consists of seven chapters.The first chapter is devoted to the introduction.In the second chapter, relations between Riccati differential equation and itssolution are given.In the third chapter, original Riccati equation is considered, and some methods aregiven to find solutions in the form of elementary functions.In the fourth chapter, fixed and movable singular points are mentioned, andcharacter of singularities of the Riccati equation is introduced.In the fifth chapter, finding methods of some special solutions of Riccati equationare given, and Riccati operator R is mentioned.In the sixth chapter, generalized Riccati equation is examined.In the seventh chapter, relations converting Riccati equation to equation in whichvariables could be separated are emphasized.

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