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A generalized non‐linear transformation for evaluating singular integrals
Author(s) -
Yun Beong In
Publication year - 2005
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.1529
Subject(s) - cauchy principal value , transformation (genetics) , mathematics , hadamard transform , principal value , singular integral , polynomial , cauchy distribution , linear map , function (biology) , order of integration (calculus) , singular value , mathematical analysis , pure mathematics , integral equation , eigenvalues and eigenvectors , boundary value problem , biochemistry , chemistry , physics , quantum mechanics , cauchy boundary condition , evolutionary biology , biology , gene , free boundary problem
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. Copyright © 2005 John Wiley & Sons, Ltd.