• 作者： 簡澄陞; 龔信有; 盧南華
• 作者服務機構： 中興大學應用數學系; 中山科學研究院
• 中文摘要： 我們研究具羅賓邊界條件的半線性特徵值問題之數值解。與其相對應的係數矩陣可表為相關的一維問題之係數矩陣的張量乘積，因而原來問題的分支解可經由一維問題的分支解求得。若把利用定義域與解的對稱性併入，我們所提的延續法算則就變得根有效率，大量的計算花費因此可被節省下來。我們亦指出一個具多參數的延續問題可利用平行計算的方法來處理。最後我們報告數值試驗的結果。
• 英文摘要： We investigate the numerical solutions of a semilinear elliptic eigenvalue problem with Robinboundary conditions. The associated coefficient matrices can be expressed as the tensor products of thecounterparts corresponding to the reduced one-dimensional problems. Thus, the solution branches of theoriginal problem may be obtained by solving the latter. The continuation algorithm proposed can be veryefficient whenever exploiting the symmetries of the domain and of the solutions are incorporated. Largeamounts of computational cost can be saved accordingly. We also indicate that a continuation problemwith multiparameters may be executed via parallel computing. Sample numerical results are reported.
• 中文關鍵字： semilinear elliptic EVP; bifurcation problem; numerical techniques; parallel compulations
• 英文關鍵字： --