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このアイテムの引用には次の識別子を使用してください: http://hdl.handle.net/10445/8040

タイトル: A Sinc method for an eigenvalue problem of a differential operator with periodic coefficients and its comparison with Hill's method
著者: Tanaka, Ken'ichiro
アブストラクト: We consider a problem of computing spectrum of an ordinary differential operator with periodic coefficients. Due to Floquet's theory, such a problem is reduced to a set of eigenvalue problems for modified operators with a periodic boundary condition. We treat two numerical methods for such problems. A first is Hill's method, which reduces each problem to a matrix eigenvalue problem with the finite Fourier series approximation of eigenfunctions of each operator. This method achieves exponential convergence rate with respect to the size of the matrix. The rate, however, gets worse as the period of the coefficients becomes longer, which is observed in some numerical experiments. Then, in order to realize accurate computation in the cases of the long periods, we propose a second method related to Sinc approximation. Basically, Sinc approximation employs Sinc bases generated by the sinc function sinc(x) = sin(pi x)/(pi x) on R. In this work, a certain variant of the sinc function is adopted to approximate periodic functions. Our method keeps good accuracy in the cases of the long periods, which can be confirmed in some numerical experiments.
研究業績種別: 国際会議/International Conference
資料種別: Conference Paper
査読有無: あり/yes
単著共著: 単著/solo
発表雑誌名,発表学会名など: Proceedings of 10th International Conference on Information Technology : New Generations
開始ページ: 179
終了ページ: 185
年月日: 2014年
出版社: IEEE
出現コレクション:田中 健一郎





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