Abstract
AbstractIn order to obtain accurate numerical evaluation of weakly singular integrals, we propose a new non‐linear co‐ordinate transformation of the sigmoidal type. The asymptotic behaviour of the present transformation near a singular point is governed by an additional parameter b≠0. Moreover, an analytical form of its inverse is derived, which is available for the case of interior‐point singularity. In the result the presented transformation can improve asymptotic truncation errors of the Gauss–Legendre quadrature rule for weakly singular integrals.By comparing the present transformation with existing sigmoidal transformations in numerical examples, we show that the former with a proper value of b can result in more accurate evaluation than the others. Copyright © 2004 John Wiley & Sons, Ltd.
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