Browsing by Author "Alusta, Fatma"
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Item SERIES SOLUTIONS OF DYNAMIC EQUATIONS ON TIME SCALES(2022-02-21) Alusta, Fatma; Erhan, İnciIn this thesis, we study the series solution method for dynamic equations on time scales. We propose a series expansion for the solution of a given dynamic equation and derive a very general recurrence relation formula for the computation of the co efficients in this series. The importance of time scales and dynamic equations on time scales shows itself in the fact that time scales unify the continuous and discrete analysis and therefore, dynamic equations cover both the differential and difference equations. In Chapter 1 we give the definition of time scales, some basic notions on time scales and present some examples. We introduce basic calculus concepts such as delta derivative and integral of function defined on time scales in Chapter 2. In the same chapter we also define some elementary functions on time scales. Chapter 3 is devoted to basic thery of linear dynamic equation of first and higher order. The Series solu tion method is presented in details in Chapter 4. In Chapter 5 we apply the method to some specific examples of linear dynamic equations including both constant and nonconstant coefficients equations. Finally, we discuss the conclussion in Chapter 6.