在本論文中，我們探討如何將半線性橢圓方程離散，利用數值分析的方法，求得數學模型的分歧點、轉彎點與正則點，並延拓出其解路徑，以探討模型的多重解的存在，有助於我們了解半線性橢圓方程在定性上的變化。本文中，我們應用了隱函數定理，並使用虛擬弧長延拓法、中央有限差商法、割線猜測法和牛頓迭代法等數值方法。

In this thesis, we use numerical methods to investigate the multiple solution paths of semilinear elliptic equations. Moreover, we research a mathematical model to find solution paths containing bifurcation points, turning points and regular points of semilinear elliptic equation. It will be helpful to understand the qualitative properties in semilinear elliptic equations. In this paper, we apply implicit function theorem. At the same time, we use numerical methods which including, pseudo–arclength continuation method, central difference method, secant predictor method and Newton’s iterative method.

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