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Uniform approximation to Cauchy principal value integrals with logarithmic singularity
http://hdl.handle.net/10098/0002000112
http://hdl.handle.net/10098/00020001123ec0f886-0168-4add-9b36-2336ca160680
名前 / ファイル | ライセンス | アクション |
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BD10126667.pdf (563 KB)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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公開日 | 2024-02-07 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | Uniform approximation to Cauchy principal value integrals with logarithmic singularity | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
資源タイプ | ||||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
資源タイプ | journal article | |||||||||
アクセス権 | ||||||||||
アクセス権 | open access | |||||||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
著者 |
Hasegawa, Takemitsu
× Hasegawa, Takemitsu
× Sugiura, Hiroshi
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抄録 | ||||||||||
内容記述タイプ | Abstract | |||||||||
内容記述 | An approximation of Clenshaw–Curtis type is given for Cauchy principal value integrals of logarithmically singular functions I(f;c)=f^1_-1 f(x)(log | x-c) / (x-c) dx (c ∈(-1,1)) with a given function f. Using a polynomial pN of degree N interpolating f at the Chebyshev nodes we obtain an approximation I(pN;c)≅I(f;c). We expand pN in terms of Chebyshev polynomials with O(N log N) computations by using the fast Fourier transform. Our method is efficient for smooth functions f, for which pN converges to f fast as N grows, and so simple to implement. This is achieved by exploiting three-term inhomogeneous recurrence relations in three stages to evaluate I(pN;c). For f(z) analytic on the interval [-1,1]in the complex plane z, the error of the approximation I(pN;c) is shown to be bounded uniformly. Using numerical examples we demonstrate the performance of the present method. | |||||||||
言語 | en | |||||||||
書誌情報 |
en : Journal of Computational and Applied Mathematics 巻 327, p. 1-11, 発行日 2018-01-01 |
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言語 | en | |||||||||
出版者 | Elsevier | |||||||||
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収録物識別子タイプ | PISSN | |||||||||
収録物識別子 | 0377-0427 | |||||||||
ISSN | ||||||||||
収録物識別子タイプ | EISSN | |||||||||
収録物識別子 | 1879-1778 | |||||||||
DOI | ||||||||||
関連タイプ | isVersionOf | |||||||||
識別子タイプ | DOI | |||||||||
関連識別子 | https://doi.org/10.1016/j.cam.2017.05.041 | |||||||||
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関連タイプ | isVersionOf | |||||||||
識別子タイプ | URI | |||||||||
関連識別子 | https://www.sciencedirect.com/science/article/pii/S0377042717302947?via%3Dihub | |||||||||
言語 | en | |||||||||
関連名称 | Science Direct | |||||||||
著者版フラグ | ||||||||||
出版タイプ | AM | |||||||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
備考 | ||||||||||
ja | ||||||||||
Science Directにてオープンアーカイブ | ||||||||||
その他のID | ||||||||||
ja | ||||||||||
TD10126667 |