本文運用微分轉換法求解各式物理系統，包括具強烈非線性之單自由度系統、非均勻軸的振動問題、擴散流動問題、Klein-Gordon問題及非線性熱傳問題等。文中首先介紹微分轉換理論的基本定義、性質及演算方法，然後在第三至八章中，分別介紹此法在各種物理問題上的應用。本文之研究內容顯示微分轉換法可用於求解具強烈非線性系統的時間響應，也可用於求解變係數微分方程之特徵值問題，而微分轉換法配合有限差分法可用於求解線性或非線性偏微分方程式。一般而言，應用微分轉換法解微分方程式時僅需很短的運算時間，而其結果與解析解做比對時只顯示出極小的誤差，由此可見微分轉換法是求解線性或非線性微分方程式的有力工具。

In this research, the differential transformation method was employed to predict the behaviors of various physical problems including the strongly nonlinear oscillators, the vibration problems of non-uniform shafts, the advective-dispersive transport problems, the nonlinear Klein-Gordon problems and some nonlinear heat transfer problems. The basic definitions and the properties of the differential transformation method were introduced briefly and the applications of this method on the physical problems were listed in the later chapters. The results of this research illustrate that the differential transformation method can be applied to solve strongly nonlinear systems. It also can be used to solve the eigenvalue problems. The hybrid method of differential transformation method and the finite difference method can be used to solve linear or nonlinear partial differential equations. In usual cases, the differential transformation method consumes only very short computing times. The errors between the simulation results and the analytical solutions were very small. The differential transformation method is a useful tool in solving linear and nonlinear equations.

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