The Euler-Maclaurin formula in presence of a logarithmic singularity

被引：5

作者：

Celorrio, R

Sayas, FJ

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, EUITIZ, E-50009 Zaragoza, Spain

[2] Univ Zaragoza, Dept Matemat Aplicada, Ctr Politecn Super, Zaragoza 50015, Spain

来源：

BIT | 1999年 / 39卷 / 04期

关键词：

Euler-Maclaurin expansions; numerical integration;

D O I：

10.1023/A:1022399409604

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this short note we prove an extension of the Euler-Maclaurin expansion for general rectangular composite quadrature rules in one dimension when the derivative of the integrand has a logarithmic singularity. We show that a correction series has to be added to the formula, but that the asymptotic expansion in powers of the discretization parameter still holds. AIMS subject classification: 65B15, 65D30.

引用

页码：780 / 785

页数：6

共 6 条

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