Improvement of the asymptotic behaviour of the Euler-Maclaurin formula for Cauchy principal value and Hadamard finite-part integrals

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In the recent works (Commun. Numer. Meth. Engng 2001; 17:881; to appear), the superiority of the non-linear transformations containing a real parameter b not equal 0 0 has been demonstrated in numerical evaluation of weakly singular integrals. Based on these transformations, we define a so-called parametric sigmoidal transformation and employ it to evaluate the Cauchy principal value and Hadamard finite-part integrals by using the. Euler-Maclaurin formula. Better approximation is expected due to the prominent properties of the parametric sigmoidal transformation of whose local behaviour near x = 0 is governed by parameter b. Through the asymptotic error analysis of the Euler-Maclaurin formula using the parametric sigmoidal transformation, we can observe that it provides a distinct improvement on its predecessors using traditional sigmoidal transformations. Numerical results of some examples show the availability of the present method. Copyright (C) 2004 John Wiley Sons, Ltd.
Publisher
Wiley-Blackwell
Issue Date
2004-09
Language
English
Article Type
Article
Keywords

WEAKLY SINGULAR-INTEGRALS; BOUNDARY-ELEMENT INTEGRALS; NUMERICAL EVALUATION; SIGMOIDAL TRANSFORMATIONS; HYPERSINGULAR INTEGRALS; GAUSSIAN QUADRATURE; CRACK PROBLEM; DERIVATIVES; EXPANSION

Citation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, v.61, no.4, pp.496 - 513

ISSN
0029-5981
URI
http://hdl.handle.net/10203/82213
Appears in Collection
MA-Journal Papers(저널논문)
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