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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

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.
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