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論文名稱 Title |
求解伯格斯方程之高階徑向基底數值法 On the high order methods for Burgers’ equation using RBFs. |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
21 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2018-01-24 |
繳交日期 Date of Submission |
2018-01-25 |
關鍵字 Keywords |
MQ擬插值函數、有限差分法、伯格斯方程 multiquadric quasi-interpolation, Burgers equation, finite-difference methods |
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統計 Statistics |
本論文已被瀏覽 5707 次,被下載 188 次 The thesis/dissertation has been browsed 5707 times, has been downloaded 188 times. |
中文摘要 |
本文介紹有限差分法與MQ擬插值函數在求解伯格斯方程之應用,並且使用高階的有限差分法結合MQ擬插值函數得到兩種延伸的高階徑向基底數值法。在一開始我們先介紹有關伯格 斯方程的相關知識,接著我們提供四種不同的演算法為將來求解伯格斯方程做準備,並且將 其應用在後面的章節,透過數值模擬可以看到這四種方法在求解伯格斯方程上的不同表現, 最後給出高階徑向基底數值法將有效改善MQ擬插值函數在伯格斯方程上的表現。 |
Abstract |
In this article, we introduce solving Burgers’s equations using finite-difference methods and multiquadric quasi-interpolation. By combining high-order finite-difference methods with multiquadric quasi-interpolation, we obtain high-order radial basis function numerical method. First we introduce the knowledge about Burgers equation, then we provide four different algorithms for solving Burgers’ s equations. And the numerical experiments justify the performance of these four methods. Finally, we conclude high-order radial basis function numerical method effectively improves the performance of multiquadric quasi-interpolation on solving Burgers’ s equations. |
目次 Table of Contents |
論文審定書i 摘要ii Abstract iii 1 引言1 2 伯格斯方程2 3 數值方法3 3.1 有限差分法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 MQ擬插值函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 二階徑向基底數值法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.4 四階徑向基底數值法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 數值實驗7 5 結論12 Reference 13 |
參考文獻 References |
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