An extrapolation method for the quadrature of functions with singularities in the vicinity of the interval of integration期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

An extrapolation method for the quadrature of functions with singularities in the vicinity of the interval of integration

Authors:	P. Midy Y. Yakovlev

Affiliation:	(1) Centre de Calcul Paris Sud Informatique, Université Paris XI, Centre d'Orsay, Bâtiment 211, F91405 Orsay, France

Abstract:	Summary A method is proposed for the calculation of integrals $I(b) = intlimits_0^A {frac{{g(x)dx}}{{(x^r + b^r )^s }}}$ and $Iprime (b) = intlimits_{ - A_1 }^{A_2 } {frac{{g(x)dx}}{{(\|x\|^r + b^r )^s }}}$ for positive small values ofb withg(x) analytic in a disk centered at the origin andr positive rational. The integrals are splitted into a singular part and a regular function ofb^r which can be extrapolated to smallb's. A principal value integral and special cases whereg(x) is not analytic at the origin are also considered.

Keywords:	AMS(MOS): 65B05 65 D 30 30 A 36 CR: 5-13, 5-16
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