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A quadrature formula for integrals with nearby singularities
Author(s) -
Tsamasphyros G.,
Theotokoglou E. E.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1649
Subject(s) - mathematics , clenshaw–curtis quadrature , gauss–kronrod quadrature formula , quadrature (astronomy) , numerical integration , gravitational singularity , gauss–jacobi quadrature , tanh sinh quadrature , mathematical analysis , gauss–laguerre quadrature , gauss–hermite quadrature , singular integral , boundary (topology) , boundary value problem , nyström method , gaussian quadrature , integral equation , physics , optics
Abstract The purpose of this paper is to propose a new quadrature formula for integrals with nearby singularities. In the boundary element method , the integrands of nearby singular boundary integrals vary drastically with the distance between the field and the source point. Especially, field variables and their derivatives at a field point near a boundary cannot be computed accurately. In the present paper a quadrature formula for ‐isolated singularities near the integration interval, based on Lagrange interpolatory polynomials, is obtained. The error estimation of the proposed formula is also given. Quadrature formulas for regular and singular integrals with conjugate poles are derived. Numerical examples are given and the proposed quadrature rules present the expected polynomial accuracy. Copyright © 2006 John Wiley & Sons, Ltd.