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題 名 | Generalized Orthogonal Polynomials Operational Matrices for Fractional Calculus and Applications=廣義正交多項式之運算矩陣及其分數微積分學上之應用 |
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作 者 | 王茂齡; 張榮語; 楊淑瑛; | 書刊名 | Journal of the Chinese Institute of Chemical Engineers |
卷 期 | 17:6 1986.11[民75.11] |
頁 次 | 頁405-410 |
分類號 | 460.02 |
關鍵詞 | 分數; 矩陣; 微積分學; 運算; 廣義正交多項式; |
語 文 | 英文(English) |
中文摘要 | 本文乃利用廣義正交多項式解分數微積分學上之問題,此種廣義正交多項式可以代表所有個別正交多項式,在本文中,首先導出廣義正交多項式之積分運算矩陣,此種廣義正交多項式積分運算矩陣之性質在運算方面與拉普拉斯(Laplace)範圍內所使用之積分子之s¯¹運算完全一樣。因此,利用此種性質,反拉普拉斯轉換便可由本文所提出簡單,準確及有效之遞廻公式計算廣義正交多項式之展開係數。由文中所示之例子得知利用本文所提供之方法將可得到非常準確之結果。 |
英文摘要 | A method of generalized orthogonal polynomials (GOP) approximation to solve the problems of fractional calculus is given. First, the operational matrices for the integration of GOP series which can represent all kinds of individual orthogonal polynomial are derived. This generalized orthogonal polynomial operational matrices perform as s¯¹ as the Laplace domain and as fractional (and operational) integration in the time domain. Based on the properties of the GOP, the expansion coefficients for the inversion of a Laplace transform are calculated in a simple, accurate and effective way through the proposed recursive formula. Very satisfactory results are obtained for the given illustrative examples. |
本系統中英文摘要資訊取自各篇刊載內容。