Regularized product intergration for Hadamard finite part integrals
type: Item
instance of: scholarly article
title: Regularized product intergration for Hadamard finite part integrals
zbMATH Open document ID: 0841.65012
DOI: 10.1016/0898-1221(95)00090-9
author: Yanyan Li
publication date: 1996-07-01T00:00:00Z
review text: This paper describes a method for the numerical computation of Hadamard finite-part integrals. The formulas developed are based on equally spaced integrand evaluation points. A novel feature of the approach taken in this paper is the use of points outside of the integration region for the construction of finite difference approximations to the integrand derivatives. Linear splines are used in the analysis of the formulas. The analysis allows for the presence of noise and the new formulas are shown to be stable if the stepsize is chosen appropriately. The convergence of the formulas is shown to be independent of the singularity exponent for the finite-part integral. Numerical results are given which demonstrate the effectiveness of the new formulas when they are applied to three example problems.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 826960
zbMATH Keywords: regularized product integration
zbMATH Keywords: singular integrals
zbMATH Keywords: linear splines
zbMATH Keywords: numerical results
zbMATH Keywords: Hadamard finite-part integrals
zbMATH Keywords: finite difference approximations
zbMATH Keywords: convergence
zbMATH Keywords: singularity exponent
reviewed by: A. Genz
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00090-9
OpenAlex ID: W2072998734
cites work: Calculating singular integrals as an ill-posed problem
cites work: Q4125663
cites work: On the solution of integral equations with strongly singular kernels
cites work: Applications of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity
cites work: Q5573683
cites work: The numerical evaluation of principal value integrals by finite-part integration
cites work: A quadrature rule for finite-part integrals
cites work: An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals
cites work: Q4100478
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 826960