Abstract
AbstractThe superiority of the use of non‐linear transformations, in numerical evaluation of the weakly singular integrals, has been recently demonstrated. In this paper, we propose a new non‐linear transformation containing a parameter which has most properties of the sigmoidal transformation. The sigmoidal behaviour of the present transformation, ΩEm(b;x) is governed not only by the order m but also by the parameter b≠0. It is shown that the presented transformation together with the Gauss–Legendre quadrature rule can better the asymptotic truncation error of the approximation effectively by controlling the value of b.Comparison of the present method with a well‐known sigmoidal transformation, in numerical examples, shows that more accurate evaluation of weakly singular integrals can be obtained so long as the number of integration points is moderately large. Copyright © 2001 John Wiley & Sons, Ltd.
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