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Series Solutions Of Dynamic Equations On Time Scales

BROWSE_DETAIL_CREATION_DATE: 19-10-2018

BROWSE_DETAIL_IDENTIFIER_SECTION

BROWSE_DETAIL_TYPE: Thesis

BROWSE_DETAIL_SUB_TYPE: Masters

BROWSE_DETAIL_PUBLISH_STATE: Unpublished

BROWSE_DETAIL_FORMAT: PDF Document

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: Mathematics,

BROWSE_DETAIL_CREATORS: Alusta, Fatma A. Abdelmula (Author),

BROWSE_DETAIL_CONTRIBUTERS: Erhan, İnci (Advisor),

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Time scales, dynamic equation, Delta derivative, series solution


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In this thesis, we study the series solution method for dynamic equations on timescales. We propose a series expansion for the solution of a given dynamic equationand derive a very general recurrence relation formula for the computation of the coecients in this series. The importance of time scales and dynamic equations ontime scales shows itself in the fact that time scales unify the continuous and discreteanalysis and therefore, dynamic equations cover both the dierential and dierenceequations.In Chapter 1 we give the definition of time scales, some basic notions on time scalesand present some examples. We introduce basic calculus concepts such as deltaderivative and integral of function defined on time scales in Chapter 2. In the samechapter we also define some elementary functions on time scales. Chapter 3 is devotedto basic thery of linear dynamic equation of first and higher order. The Series solutionmethod is presented in details in Chapter 4. In Chapter 5 we apply the methodto some specific examples of linear dynamic equations including both constant andnonconstant coecients equations. Finally, we discuss the conclussion in Chapter 6.


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