佐藤超函数論に基づく数値解析  [in Japanese] Numerical Analysis Based on the Hyperfunction Theory  [in Japanese]

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Abstract

<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>

Journal

  • Bulletin of the Japan Society for Industrial and Applied Mathematics

    Bulletin of the Japan Society for Industrial and Applied Mathematics 27(4), 8-15, 2018

    The Japan Society for Industrial and Applied Mathematics

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