Euler-Maclaurin Expansions and Approximations of Hypersingular Integrals
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.
C. Hu et al., "Euler-Maclaurin Expansions and Approximations of Hypersingular Integrals," Discrete and Continuous Dynamical Systems - Series B, vol. 20, no. 5, pp. 1355 - 1375, American Institute of Mathematical Sciences (AIMS), Jul 2015.
The definitive version is available at https://doi.org/10.3934/dcdsb.2015.20.1355
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Arbitrary Singular Point; Euler-Maclaurin Expansion; Extrapolation; Hypersingular Integral; Mid-Rectangular Quadrature Formula
International Standard Serial Number (ISSN)
Article - Journal
© 2015 American Institute of Mathematical Sciences (AIMS), All rights reserved.
01 Jul 2015