Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18151
標題: 一些變異的雙重網格離散法處理半線性橢圓特徵值問題
Some variants of the two-grid discretization method for semilinear elliptic eigenvalue problems
作者: 葉政叡
Yeh, Cheng-Jui
關鍵字: semilinear elliptic eigenvalue problems
半線性橢圓特徵值問題
bifurcation points
continuation methods
two-grid schemes
Lanczos method
分歧點
延續法
雙重網格法
Lanczos方法
離散法
特徵值
差分法
演算法
所得
出版社: 應用數學系
摘要: 我們討論雙重網格法應用在延續法中,來解半線性橢圓特徵值問題。我們使用中央差分法來離散化這些問題,並且使用前置Lanczos法來解線性系統。同時我們對雙重網格延續演算法做一些變異,亦可找出半線性橢圓特徵值問題的曲線。由數值的結果證明我們提供的演算法使雙重網格延續法在處理半線性橢圓特徵值問題時更加堅固、健全。最後我們將所得結果繪製成圖表並做結論。
We present some variants of the two-grid discretization schemes with two-loop continuation algorithm for tracing solution branches of semilinear elliptic eigenvalue problems. We show that a singular point on the coarse grid solution branch can be well approximated by considering the linear and quadratic approximations of the operator equation on the fine grid. Then we indicate some possibilities of implementing the corrector step in the inner continuation of the two-grid discretization schemes. Numerical implementations of the proposed algorithms are reported. A comparison between the performance of the proposed two-grid discretization methods is given.
URI: http://hdl.handle.net/11455/18151
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