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Numerical quadrature for computing of singular integrals.
- Source :
-
Journal of Numerical Mathematics . Jun2015, Vol. 23 Issue 2, p175-193. 19p. - Publication Year :
- 2015
-
Abstract
- The paper is concerned with the superconvergence of numerical evaluation of Hadamard finite-part integral. Following the works [6-9], we studied the second-order and the third-order quadrature formulae of Newton-Cotes type and introduced new rules. The rule for the second-order gives the same convergence rate as the rule [6] but in more general cases, the rule for the third-order gives better results than the rule in [9] In this work, first we mention the main results on the superconvergence of the Newton-Cotes rules, we mention trapezoidal and Simpson's rules and then we introduce a rule based on the cubic approximation. In the second part we describe important error estimates and in the last section we demonstrate theoretical results by numerical examples. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15702820
- Volume :
- 23
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 108798064
- Full Text :
- https://doi.org/10.1515/jnma-2015-0012