臺灣博碩士論文加值系統

在本文中,我們利用中央差分法,牛頓迭代法,虛擬弧長延拓法及有限維的Liapunov-Schmid
t降階法等數值方法,配合分歧理論的基礎--隱函數定理,對非線性分歧問題中的非線性特
徵值問題討論解路徑之延拓與分歧.並針對幾個數學模型,例如Rod buckling problem,Rea
cion-Diffusion problem及半線性橢圓特徵質問題進行探討;從而求得包含正則點,轉彎點
及分歧點的解分支和解路徑,有助於對非線性分歧問題之定性分析的進一步了解.

In this thesis,we use numerical methods which including central difference met
hod,Newton''s iteration method,pesudo-arclength method and finite dimensional L
iapunov-Schmidt deflation method,and discuss both continuation and bifurcation
of solution path in the nonlinear eigenvalue problems of nonlinear bifurcatio
n problems compound with the basis of bifurcation theory-implicit function the
orem. At the same time,we research several mathematics models such as Rod bucl
ing problem,Reaction-Diffusion problem and semi-linear elliptic eigenvalue pro
blem in order to find the solution branches and solution pathes including regu
larpoints,turing points and bifurcation points which are helpful to the unders
tanding of qualitative analysis in the nonlinear bifurcation problems.