Kirkup, Stephen M. and Yazdani, Javad and Papazafeiropoulos, George (2019) Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the <i>x = t<sup>p</sup></i> Substitution. American Journal of Computational Mathematics, 09 (04). pp. 282-301. ISSN 2161-1203
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Abstract
Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.
Item Type: | Article |
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Subjects: | Digital Academic Press > Mathematical Science |
Depositing User: | Unnamed user with email support@digiacademicpress.org |
Date Deposited: | 17 Jun 2023 06:32 |
Last Modified: | 18 Jun 2024 07:14 |
URI: | http://science.researchersasian.com/id/eprint/1486 |