臺灣博碩士論文加值系統

摘 要
本篇論文主要在探討ㄧ個非等溫擴散反應模型的分支點計算及其解路徑延拓的特性﹒
我們將以隱函數定理為基礎﹐利用打靶法和牛頓迭代法來計算出分歧點或轉彎點.接著使用Liapunov-schmidt降階法﹑切線猜測法﹑割線猜測法和虛擬弧長延拓法等數值方法﹐來找出我們的模型在各參數有限範圍內之解路徑情形﹐並試著改變各參數進而延拓出通過分支點的解分支路徑﹒

Abstract
This paper mainly discuss the continuation of solution paths and the computation of branching points of non-isothermal diffusion and reaction model.
We use the implicit function theorem as the foundations,and use the shooting method and the Newton's interative method to calculate bifurcation points or turning points. Also, we use the numerical methods of liapunov-schmidt reduction method,tangent-predictor method, secant-predictor method and pseudo-arclength continuation method to find out the multiple solutions within limited range of parameters. Finally, we try to change various parameters to continue all Solution branches from Bifurcation points.

目 錄
第一章 緒論--------------------------------------- 1

第二章 分歧理論與延拓法-----------------------------3
2.1 分歧問題--------------------------------------- 3
2.2 隱函數定理與分歧理論---------------------------- 6
2.3 局部延拓法-------------------------------------- 8
2.4 虛擬弧長延拓法---------------------------------- 11

第三章 非線性方程組之分支點與解分支----------------- 14
3.1 分支點之求法-------------------------------------14
3.2 選取分支點解分支之延拓方向 ---------------------- 26
3.3 解分支的延拓------------------------------------ 33
3.4 演算法------------------------------------------36

第四章 數值實驗----------------------------------- 41
實驗(一)-------------------------------------------- 42
實驗(二)-------------------------------------------- 68
實驗(三)-------------------------------------------- 85

第五章 結論----------------------------------------- 92

參考文獻-------------------------------------------- 94

參考文獻
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