臺灣博碩士論文加值系統

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.