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田中 健一郎 >

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/10445/8044

タイトル: A fast and accurate numerical method for the symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula
著者: Tanaka, Ken'ichiro
アブストラクト: In this paper, we propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar L\'evy processes. The method is based on the accurate numerical formulas for Fourier transform proposed by Ooura. These formulas are combined with nonuniform fast Fourier transform (FFT) and fractional FFT to speed up the numerical computations. Moreover, we propose a formula for numerical indefinite integration on equispaced grids as a component of the method. The proposed integration formula is based on the sinc-Gauss sampling formula, which is a function approximation formula. This integration formula is also combined with the FFT. Therefore, all steps of the proposed method are executed using the FFT and its variants. The proposed method allows us to be free from some special treatments for a non-smooth initial condition and numerical time integration. The numerical solutions obtained by the proposed method appeared to be exponentially convergent on the interval if the corresponding exact solutions do not have sharp cusps. Furthermore, the real computational times are approximately consistent with the theoretical estimates.
研究業績種別: その他/Others
資料種別: Preprint
査読有無: なし/no
単著共著: 単著/solo
発表雑誌名,発表学会名など: arXiv:1408.0157
年月日: 2014年8月
出現コレクション:田中 健一郎

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