A generalized non-linear transformation for evaluating singular integrals

In this paper, we propose a function which, according to a parameter included therein, generates a new sigmoidal transformation and converges to the well-known Sato polynomial transformation. Following well-established procedures in the literature, we employ the present transformation in the numerical evaluation of weakly singular integrals, Cauchy principal value integrals and Hadamard finite-part integrals. By several numerical examples it is shown that the present transformation is available for all kinds of singular integrals mentioned above and, in some cases, gives better results compared with those of traditional non-linear transformations