臺灣博碩士論文加值系統

本論文旨在數值探討一個化學熱質轉換模型的分歧問題.
首先,我們以隱函數定理為基礎,推導計算出分歧點,再利用打靶法,牛頓迭代法,虛擬弧長延拓法及割線猜測法等數值方法,來延拓出所有通過分歧點的解分支路徑.
最後,我們藉由改變各種參數,觀察解路徑上的分歧現象與分歧點的變化.

The purpose of this paper is to numerically investigate bifurcation problems in a chemical heat and mass transfer model.
First, we base on implicit function theorem to calculate the bifurcation points and then get the path of all that passing through the bifurcation points with the shooting method, Newton’s iterative method, Pseudo-arclength continuation method and secant predictor and so on.
Finally, we observe bifurcation phenomenons at bifurcation points with different parameters.

第一章 緒論 -1
第二章 分歧理論與虛擬弧長延拓法 -3
2.1 分歧問題 -3
2.2 隱函數定理與分歧理論 -5
2.3局部延拓法 -7
2.4 牛頓迭代法 -9
2.5 虛擬弧長延拓法 -10
第三章 非線性常微分方程的分歧點與解分支 -12
3.1 分歧點之求法 -12
3.1.1 解非線性常微分方程組的分支點-牛頓法 -12
3.1.2 非線性常微分方程邊界值問題的分歧點 -14
3.2 選取分歧點的解分支方向 -20
3.2.1 Liapunov-schmidt降階法 -20
3.2.2 選取解分支延拓方向 -23
3.2.3 選取各解分支延拓方向的初始猜值 -26
3.3 解分支的延拓 -27
3.3.1 虛擬弧長延拓法之數值計算 -27
3.3.2 割線預測法與牛頓迭代法求解路徑 -28
3.4 演算法 -29
第四章 數值實驗 -33
4.1 實驗(4.1) -33
4.2 實驗(4.2)改變 值 -57
4.3 實驗(4.3)改變 值 -86
第五章 結論 -96
參考文獻 -97

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