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Evaluations of certain hypersingular integrals on interval
Author(s) -
Du QiKui
Publication year - 2001
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.218
Subject(s) - hadamard transform , simple (philosophy) , computation , mathematics , interval (graph theory) , point (geometry) , numerical analysis , calculus (dental) , mathematical analysis , algorithm , geometry , combinatorics , medicine , philosophy , dentistry , epistemology
In this paper, we investigate a hypersingular integral on an interval. The definition of Hadamard's finite‐part integrals and some of its properties are given. Some numerical methods on approximate computation of the finite‐part integrals are constructed. The new method is very simple, easy to implement, reliable, and above all, not affected by the location of singular point. Some numerical experiments are carried out using the current formulae, and numerical results show that the current methods are feasible and effective. Copyright © 2001 John Wiley & Sons, Ltd.