Numerical integration based on hyperfunction theory
Numerical integration based on hyperfunction theory
复制标题
基于超函数理论的数值积分
DOI：
10.1016/j.cam.2017.06.018
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
Hirayama Hiroshi
中科院分区：
文献类型：
--
作者：
Ogata Hidenori;Hirayama Hiroshi
在本文中，我们提出了超函数理论在数值积分中的应用。超函数理论是函数理论的广义版本，其中具有奇点（例如极点、不连续性和δ脉冲）的函数用复解析函数来表示。超函数理论的这一特征使我们能够构建解析函数的数值积分方法。理论误差估计表明我们的方法在几何上收敛，数值例子表明我们的方法非常有效，特别是对于具有强端点奇点的积分。此外，我们提出了一种基于超函数方法的自动积分方法。
In this paper, we propose an application of hyperfunction theory to numerical integration. Hyperfunction theory is a generalized version of function theory where functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex analytic functions. This feature of hyperfunction theory allows us to construct a numerical integration method for analytic functions. Theoretical error estimates show that our method converges geometrically, and numerical examples show that our method is very efficient especially for integrals with strong end-point singularities. In addition, we present an automatic integration method based on our hyperfunction method.