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Article
Euler-Maclaurin Expansions and Approximations of Hypersingular Integrals
Discrete and Continuous Dynamical Systems - Series B
  • Chaolang Hu
  • Xiaoming He, Missouri University of Science and Technology
  • Tao Lü
Abstract
This article presents the Euler-Maclaurin expansions of the hypersingular integrals [image] with arbitrary singular point t and arbitrary non-negative integer m. These general expansions are applicable to a large range of hypersingular integrals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions.
Department(s)
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
  • Arbitrary Singular Point,
  • Euler-Maclaurin Expansion,
  • Extrapolation,
  • Hypersingular Integral,
  • Mid-Rectangular Quadrature Formula
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 American Institute of Mathematical Sciences, All rights reserved.
Publication Date
7-1-2015
Citation Information
Chaolang Hu, Xiaoming He and Tao Lü. "Euler-Maclaurin Expansions and Approximations of Hypersingular Integrals" Discrete and Continuous Dynamical Systems - Series B Vol. 20 Iss. 5 (2015) p. 1355 - 1375 ISSN: 15313492
Available at: http://works.bepress.com/xiaoming-he/14/