本文運用微分轉換法結合有限差分法於考慮規則外型與不規則外型邊界下求解非線性及非均質熱傳導問題。同時，亦運用微分轉換法結合有限差分法於求解雙曲線型熱傳導問題。文中首先介紹微分轉換理論的基本定義、性質及演算方法，然後介紹此法混合有限差分法在各種熱傳導問題上的應用。
　　研究結果顯示運用微分轉換混合有限差分法不管在規則外型或不規則外型邊界下皆能兼具效率及準確性的求解非線性及非均質熱傳導問題。此外，以微分轉換混合有限差分法亦可應用於求解雙曲線型熱傳導問題，並得到良好的模擬結果。經由選取一適當的差分格點數後將能有效抑制位於熱傳波前陡峭不連續處的數值振盪現象發生。一般說來，使用微分轉換法進行模擬求解與其他方法相比較所需的運算處理時間較為短暫。有別於以往運用積分運算求解的方法，以微分轉換法求解各類熱傳導問題省去了冗長及繁雜的變換程序，不僅顯得簡易且將更具系統性。

　In this research, the hybrid method which combines differential transformation and finite difference approximation techniques was employed to solve nonlinear heat conduction problems and non-homogeneous heat conduction problems in regular and irregular regions. Moreover, the use of a hybrid method which combines differential transformation and finite difference approximation was also employed to solve hyperbolic heat conduction problems. The basic definitions and properties of the differential transformation method were introduced briefly and the applications of this method on the heat conduction problems were displayed later.
　The results of this research show that the hybrid method of differential transformation and finite difference methods can be used to solve nonlinear and non-homogeneous heat conduction problems accurately and efficiently whether in regular or irregular region. Besides this, the hybrid method of differential transformation and finite difference can also be applied to solve the hyperbolic heat conduction problems for good results. The oscillations which arise in the vicinity of sharp discontinuities can be successfully suppressed by calculating with an appropriate number of grids. In usual case, applying the hybrid method on the simulation procedure consumes less CPU time as compared with other methods. Unlike other integral transform methods, using the differential transform to solve heat conduction problems leaves out the copious and complex transform procedure and appears not only brief but also more systematical.

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