Euler-Maclaurin Expansions and Approximations of Hypersingular Integrals

Author

Chaolang Hu
Xiaoming He, Missouri University of Science and TechnologyFollow
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.

Recommended Citation

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

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

International Standard Serial Number (ISSN)

1531-3492

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Jul 2015