数値積分に対する超函数法  [in Japanese] Hyperfunction Method for Numerical Integrations  [in Japanese]

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<p><b>概要.</b> 本論文では,平山が提案した有限区間積分に対する数値積分法 —本論文では「超函数法」と呼ぶ —について解析を行う.超函数法では,問題とする積分を閉積分路上の複素積分に変換して,周期関数に対して性能の良い台形公式で近似計算する.数値実験により,超函数法は積分区間端点の特異性が強い積分に対して有効であることがわかる.また,超函数法と佐藤超函数論との関係についても触れる.</p>

<p><i>Abstract.</i> We examine Hirayama's numerical integration method for integrals over finite intervals, which is called the "hyperfunction method" in this paper. In the hyperfunction method, an integral is transformed into a complex integral on a closed contour and is approximated by the trapezoidal rule,which gives good results for integrals in the case that the integrands are periodic functions. Numerical examples show that the hyperfunction method is effective for integrals with strong end-point singularities. We also remark that the relation between the hyperfunction method and the hyperfuction theory.</p>

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 26(1), 33-43, 2016

    The Japan Society for Industrial and Applied Mathematics

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