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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Quadrature formulae for Cauchy principal value integrals of oscillatory kind


Author: G. E. Okecha
Journal: Math. Comp. 49 (1987), 259-268
MSC: Primary 65D32; Secondary 41A55
DOI: https://doi.org/10.1090/S0025-5718-1987-0890267-X
MathSciNet review: 890267
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Abstract: The problem considered is that of evaluating numerically an integral of the form $ f_{ - 1}^1\;{e^{i\omega x}}f(x)\,dx$, where f has one simple pole in the interval $ [ - 1,1]$. Modified forms of the Lagrangian interpolation formula, taking account of the simple pole are obtained, and form the bases for the numerical quadrature rules obtained. Further modification to deal with the case when an abscissa in the interpolation formula is coincident with the pole is also considered. An error bound is provided and some numerical examples are given to illustrate the formulae developed.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0890267-X
Keywords: Lagrangian interpolation, orthogonal polynomials, oscillatory integrals, Cauchy principal value, Legendre polynomials, error bound
Article copyright: © Copyright 1987 American Mathematical Society