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URN etd-0903110-132432 Author Yin-wei Lin Author's Email Address timothy@math.nsysu.edu.tw Statistics This thesis had been viewed 5168 times. Download 1057 times. Department Applied Mathematics Year 2009 Semester 2 Degree Ph.D. Type of Document Language English Title Theory and Calculation of Iterative Functional Differential Equation Date of Defense 2010-07-23 Page Count 166 Keyword delay state-dependent analytic solution Abstract Functional differential equations with delay have long been studied due to their practical applications. For the delay term is not a constant number, many researches study the case when this deviating argument depends on the state variable. So we deal with the differential and functional equations involving with the compositions of the unknown function, i.e. the iterative functional differential equations (IFDEs) and iterative functional equations (IFEs) without derivative. The main purpose of this dissertation is to investigate the solutions of such equations, including their analytic solutions, numerical solutions and qualitative behaviors.

First, we survey some well known differential equations of this type which possess analytic solutions. Then the classical method of undetermined coefficients is used to compute these power series solutions for the first order IFDEs in Chapter 1, the second order IFDEs in Chapter 2 and FDEs in Chapter 3. Taylor series method is also used to get these analytic solutions in Chapter 4. Systematical method is found to locate the fixed point in generalized sense, so we can use these methods to calculate the coefficients of their analytic solutions. Furthermore, we also establish the existence and uniqueness theorem for analytic solution in Chapter 5.

Second, we survey the known existence and uniqueness theorems of solutions for these IFDEs and FDEs in Chapter 6. Then we apply Schauder fixed point theorem to establish new existence theorems of local solutions for general IFDEs. Under certain conditions, these local solutions can be extended to global solutions.

Chapter 7 deals with the simplest IFDEs the Eder's equation. We extend the qualitative properties of this case and find its solution is not unique. In Chapter 8, we use Euler method to get the numerical solution of IFDEs. Under some conditions, we have the error analysis on these equations. In Chapter 9, we employ the method of undetermined coefficients, Taylor series, Picard's iteration and Si's methods to get their analytic solutions. Their comparisons, the advantage and disadvantage of these methods are also discussed.Advisory Committee Zi-cai Li - chair

Shih-chung Chiang - co-chair

Hung-tsai Huang - co-chair

Chieh-sen Huang - co-chair

Tzon-Tzet Lu - advisor

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etd-0903110-132432.pdf Date of Submission 2010-09-03