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研究生: 馮桂蓮
論文名稱: 具Brusselator反應的三結合核模型之分歧問題探討
Numerical Investigation for the Bifurcation Problems of Three Coupled Cells with Brusselator Reaction
指導教授: 簡國清
口試委員:
學位類別: 碩士
Master
系所名稱:
論文出版年: 2006
畢業學年度: 95
語文別: 中文
論文頁數: 96
中文關鍵詞: 隱函數定理牛頓迭代法局部延拓法虛擬弧長延拓法轉彎點分歧點
外文關鍵詞: Implicit theorem, Newton iterative method, Local continuation method, Pseudo-arclength mehod, Turning point, Bifurcation point
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  • 摘 要
    在本文中,我們以分歧理論的基礎—隱函數定理為基本工具,利用割線預測法、牛頓迭代法和擬弧長延拓法等數值方法,來對一具Brusselator反應之三結合核模型的解路徑做數值探討。對參數在正值及負值的解路徑圖進行分析,並求得其轉彎點和分歧點。


    Abstract
    In this paper, we use the implicit function theorem, secant predictor method, Newton iterative method and pseudo-arclength continuation method to investigate the bifurcation problems of three couple cells with Brusselator reaction. Finally, we analyze the solution paths of the model and find the turning points and bifurcation points of the model.

    目 錄 第一章 緒論 1 第二章 分歧理論與延拓法 4 2.1 分歧理論 4 2.2 分歧問題 6 2.3 延拓法 8 2.3.1 局部延拓法 8 2.3.2 虛擬弧長延拓法 10 第三章 非線性代數方程問題的數值方法 12 3.1解路徑的數值解法及牛頓迭代法 12 3.2局部延拓法 14 3.3虛擬弧長延拓法之數值計算 15 第四章 數值實驗 17 4.1非線性代數方程解路徑之延拓 17 4.1.1自然局部延拓法演算法 17 4.1.2虛擬弧長延拓法演算法 18 4.2實驗結果 20 實驗一:取 為正值時, 到 的解路徑 20 實驗二:取 為負值時, 到 的解路徑 38 第五章 結論 94 參考文獻 95

    參考文獻

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