佐藤超函数論に基づく数値解析

DOI
  • 緒方 秀教
    電気通信大学大学院・情報理工学研究科・情報・ネットワーク工学専攻

書誌事項

タイトル別名
  • Numerical Analysis Based on the Hyperfunction Theory

抄録

<p>In this paper, we show an application of hyperfunction theory to numerical integration. It is based on the remark that, in hyperfunction theory, functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex holomorphic functions. In our method, we approximate a desired integral by approximating the complex integral which defines the desired integral as an hyperfunction integral by the trapezoidal rule. Theoretical error analysis shows that the approximation by our method converges geometrically, which is due to the fact that the approximation by the trapezoidal rule of the integral of a periodic analytic function over one period interval or the integral of an analytic function over the whole infinite interval converges geometrically. Numerical examples show that our method is efficient especially for integrals with strong end-point singularities.</p>

収録刊行物

  • 応用数理

    応用数理 27 (4), 8-15, 2017-12-22

    一般社団法人 日本応用数理学会

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詳細情報 詳細情報について

  • CRID
    1390001205765195776
  • NII論文ID
    130006594794
  • DOI
    10.11540/bjsiam.27.4_8
  • ISSN
    24321982
  • 本文言語コード
    ja
  • データソース種別
    • JaLC
    • CiNii Articles
    • KAKEN
  • 抄録ライセンスフラグ
    使用不可

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