On the Filon and Levin methods for highly oscillatory integral ∫ab f(x)eiωg(x) dx

被引：24

作者：

Xiang, Shuhuang ^{[1
]}

机构：

[1] Cent S Univ, Dept Math, Changsha 410083, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 208卷 / 02期

基金：

日本学术振兴会;

关键词：

oscillatory integral; filon method; Levin method;

D O I：

10.1016/j.cam.2006.10.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper shows that for any suitably smooth function f(x) and arbitrarily selected interpolation nodes c(1), c(2),..., c(v), in [a, b], the Filon method and the Levin method for integral(b)(a) f(x)e(i omega g(x)) dx with the polynomial interpolation approach are identical when g(x) is a linear function. Based on this result, a new efficient Levin quadrature for integral(a)(b) f(x)e(i omega g(x)) dx is presented. (C) 2006 Published by Elsevier B.V.

引用

页码：434 / 439

页数：6

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