• 作者： 王茂齡
• 作者服務機構： 國立清華大學化學工程學系
• 中文摘要： 本篇論文報導一個可以結合任意正交多項式於一體之廣義正交多項式(GOP)，藉以代表各種正交多項式應用於解決系統科學上之方法，其關鍵性之觀念在於應用正交多項式與幕次級數之間的關係，推導出各種運算矩陣，並將其應用到解各種動態系統問題上。由於這些運算矩陣能夠概括所有的正交多項式，因此，可充分地利用每個正交多項式之不同特性，經過適當的選擇與轉換後，應用到工程科學問題上，以期達到簡化演算策略，縮短運算時間和提高結果正確性的要求。
• 英文摘要： In this paper, the generalized orthogonal polynomials (GOP), which can be used to represent allkinds of individual orthogonal polynomials and non-orthogonal Taylor series are introduced to solve theproblems of systems science. The key idea is to derive a uniform form of operational matrix ofthe generalized orthogonal polynomials by using the relation between orthogonal polynomials and powerseries. The kind of operational matrix of the generalized orthogonal polynomials can cover thecharacteristics of all different types of the individual orthogonal polynomial. Therefore, the simplificationof computation algorithms and the saving of computer time as well as an increase in the accuracyof computation results for solving the problems of dynamic systems are achieved using this special form ofoperational matrix of GOP with appropriate selection of GOP and transformation.
• 中文關鍵字： generalized orthogonal polynomial; operationa; matrices
• 英文關鍵字： --