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題名 | An Improved Maple Package for Computing Contact Symmetries of Differential Equations=計算微分方程之接觸對稱的改進的Maple程序包 |
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作者姓名(中文) | 張哲瑋; 鄭博仁; | 書刊名 | 遠東學報 |
卷期 | 27:4 2010.12[民99.12] |
頁次 | 頁377-388 |
分類號 | 314.22 |
關鍵詞 | 接觸對稱; 微分方程; 電腦代數系統; Contact symmetry; Differential equations; Computer algebra system; |
語文 | 英文(English) |
中文摘要 | 本文介紹一個改良的Maple程序包,此程序包可以自動計算微分方程的接觸對稱。接觸李群為其無窮小生成元依賴於獨立變數、因變數及其一階導數的局部變換,會保持在此變換下的相切方程式(稱為接觸條件)不變。改良的程式架構於Maple平台,主要目的是比Maple內建的函數找出更多微分方程的接觸對稱。本文並以例子來測試本改良的程序包,並與利用Maple 14內建的函數 Infinitesimals 以及由A. F. Cheviakov 所發展的GeM (v.0.31)程序包[5]所得的計算結果進行比較,用以驗證本程序包的適用性與有效性。此外,本文亦以實例介紹接觸對稱在常微分方程之降階上的應用。 |
英文摘要 | In this thesis, we present an improved Maple package to automate the computation of contact symmetries of differential equations. Lie Groups of contact transformations are the local transformations with the infinitesimal generators depending on the independent and dependent variables as well as the first-order derivatives of dependent variables, such that the tangency (contact) conditions are preserved. This improved package is based upon the computer algebra system Maple, and its purpose is to find more infinitesimal generators of Lie Groups of contact transformations admitted by a given DE than the original Maple package can possibly get. We compare the effectiveness of our package with the function Infinitesimals in Maple 14 and the package GeM (v. 0.31) developed by A. F. Cheviakov [5] by a number of examples. Finally, two examples are illustrated to demonstrate the application of contact symmetries to reduction of order of ODEs. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。