本論文主要在探討一個超導模板模型解路徑之分歧問題.
首先,在隱函數定理的基礎下,計算出分歧點與轉彎點,再利用切線猜測法,割線猜測法,牛頓迭代法及虛擬弧長延拓法…等數值方法,討論其分歧現象及延拓出所有通過分歧點或轉彎點的解分支路徑.
最後,藉由改變各種參數,觀察解路徑上分歧點及轉彎點的變化情形,並求得含有分歧點、轉彎點的解路徑與解分支圖,來探討解路徑圖上的分歧現象,以了解超導模板模型分歧問題的變化.

The main purpose of this thesis is to investigate bifurcation problems of solution paths in a Superconducting Slab Model.
First, apply the implicit function theorem to calculate the bifurcation points or turning points and then use the tangent predictor, secant predictor, Newton’s iterative method, and Pseudo- Arclength Continuation method and so on to discuss the bifurcation problems and get the solution paths, which passes through all of the bifurcation points or turning points of the solution branch paths.
Finally, by changing the different parameters observe the variations of the bifurcation points and turning points of the solution and derive solution paths, and the solution branches diagram from the bifurcation points and turning points. Investigate the solution path diagram of the branch phenomenon to understand the bifurcation problems in a Superconducting Slab Model.

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