Modified Sinc-collocation methods for integral equations of the second kind and their theoretical analysis(Theory)

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  • Okayama Tomoaki
    Graduate School of Information Science and Technology, University of Tokyo
  • Matsuo Takayasu
    Graduate School of Information Science and Technology, University of Tokyo
  • Sugihara Masaaki
    Graduate School of Information Science and Technology, University of Tokyo

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Other Title
  • 第二種積分方程式に対するSinc選点法の改良とその理論解析(理論)
  • 第二種積分方程式に対するSinc選点法の改良とその理論解析
  • ダイ2シュ セキブン ホウテイシキ ニ タイスル Sincセンテンホウ ノ カイリョウ ト ソノ リロン カイセキ

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In this paper the Sinc-collocation methods for integral equations of the second kind proposed by Rashidinia and Zarebnia in 2005 and 2007 are improved in the following two senses. 1) The Rashidinia-Zarebnia scheme is modified so that it can be implemented under more practical conditions. Then its convergence is proved in a rigorous manner. 2) A new scheme is developed by replacing the single exponential transformation in the Rashidinia-Zarebnia scheme with the double exponential transformation. Then it is shown both numerically and theoretically that the new scheme is far more accurate than the (modified) Rashidinia-Zarebnia scheme.

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