Chebyshev collocation method 是一種用來找出高階線性積分微分方程系統的數值解的矩陣解法，這種解法使用truncated Chebyshev series 及Chebyshev collocation points將原來的系統及其邊界條件轉換成矩陣方程式。它除了能找出積分微分方程的數值解外，有時也能求出正確解。因為這種方法所構造的矩陣相當大，所以我們必須配合數學軟體來使用。

A matrix method called the Chebyshev collocation method is used to solve a systems of higher-order linear integro-differential equations numerically. We use truncated Chebyshev series and Chebyshev collocation points to transform the systems of integro-differential equations and the given conditions into the matrix equations . The method can be proposed to obtain approximate solution and analytical solution of IDEs .Since size of the matrices created by the method are large ,this allow us to use mathematical software .

CHINESE ABSTRACT....... Ⅰ
ENGLISH ABSTRACT....... Ⅱ
ACKNOWLEDGEMENT ....... Ⅲ
CONTENTS............... IV
CHAPTER 1.INTRODUCTION .......1
CHAPTER 2.FUNDAMENTAL RELATIONS.......4
CHAPTER 3.THE METHODS OF THE SOLUTION.......11
CHAPTER 4.ILLUSTRATION.......19
CHAPTER 5.CONCLUSION.......39
REFERENCES.......40

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