Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631329 | Applied Mathematics and Computation | 2012 | 14 Pages |
Abstract
A new automatic quadrature scheme is proposed for evaluating Cauchy principal value integrals of oscillatory functions: â¨-11f(x)exp(iÏx)(x-Ï)-1dx(-1<Ï<1,ÏâR). The desired approximation is obtained by expanding the function f in the series of Chebyshev polynomials of the first kind, and then by constructing the indefinite integral for a properly modified integrand, to overcome the singularity. The method is proved to converge uniformly, with respect to both Ï and Ï, for any function f satisfying maxâ1⩽x⩽1â£fâ²(x)â£Â < â.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
PaweÅ Keller,