Article ID Journal Published Year Pages File Type
1710397 Applied Mathematics Letters 2007 8 Pages PDF
Abstract

We consider a Gaussian type quadrature rule for some classes of integrands involving highly oscillatory functions of the form f(x)=f1(x)sinζx+f2(x)cosζxf(x)=f1(x)sinζx+f2(x)cosζx, where f1(x)f1(x) and f2(x)f2(x) are smooth, ζ∈Rζ∈R. We find weights σνσν and nodes xν,ν=1,2,…,nxν,ν=1,2,…,n, in a quadrature formula of the form ∫−11f(x)dx≈∑ν=1nσνf(xν) such that it is exact for all polynomials f1(x)f1(x) and f2(x)f2(x) from Pn−1Pn−1. We solve the existence question, partially.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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