本論文主要在探討非線性邊界值常微分方程組之轉彎點,分歧點與其解分支結構.
首先,我們利用打靶法及牛頓迭代法,來推導計算出分歧點或轉彎點.並以隱函數定理為基礎,運用Liapunov-schmidt降階法,虛擬弧長延拓法,割線猜測法及牛頓迭代法等數值方法,來延拓出所有通過分歧點的解分支路徑.
最後,我們改變其中一參數,而將其他參數固定,分別求得分歧現象,分歧點與轉彎點的變化.

This thesis investigates the turning points, bifurcation points and solution branches of nonlinear ordinary differential equations with the boundary-values.
First, we use shooting method and newton’s interative method to calculate the bifurcation points or turning points.We use implicit function theorem as the foundation to quote the numerical method of the Liapunov-Schmidt reduction method, pseudo-archength continuation method, secant-predictor method, and Newton’s interative method,to continue all solution branches from bifurcation points.
Finally, we change one of the parameters and fix the others to find the bifurcation phenomenon, and the changes of bifurcation points and turning points.

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