Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18203
標題: 利用對稱性探討具紐依曼邊界條件的半線性橢圓問題
Exploiting Symmetries for Semilinear Elliptic Problems with Neumann Boundary Conditions
作者: 鄭博文
Jeng, Bor-Wen
關鍵字: Lanczos method
蘭求斯方法
symmetry
continuation method
bifurcation
Neumann problems
finite differences
對稱性
延續法
分枝
紐依曼問題
有限差分法
出版社: 應用數學系
摘要: 我們利用對稱性探討某些具紐依曼邊界條件的半線性特徵值問題之解曲線 。我們證明對稱性讓原問題分解成定義在子區域的縮小問題;且經中央差 分法離散化,對應於 Laplacian運算子的係數矩陣相似於一個對稱矩陣。 而且離散化的問題保有原連續問題一些關於特徵值的基本性質。因此在以 前所倡導的延續﹣Lanczos 算則可被修正,用以追蹤縮小問題的解曲線。 最後,我們對數值結果提出報告。
We exploit symmetries in certain semilinear elliptic eigenvalue problems withNeumann boundary conditions for the continuation of solution curves. We showthat symmetry makes the problem decomposable into small ones, and thediscretization matrix obtained via central differences associated to theLaplacian is similar to a symmetric one. Furthermore, the discrete problemspreserve some basic properties on eigenvalues of the continuous problems.Thus the continuation-Lanczos algorithm can be adapted to trace the solutioncurves of the reduced problems. Sample numerical results are reported.
URI: http://hdl.handle.net/11455/18203
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