Year: 2019
Author: Hui Feng, Yan Gao, Lili Ju, Xiaoping Zhang
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 240–254
Abstract
In this paper, we study a new nodal-type trapezoidal rule for approximating Hadamard finite-part integrals, and its application to numerical solution of certain finite-part integral equation. We start with a nodal-type trapezoidal rule discussed in [21], and then establish its error expansion analysis, from which a new nodal-type trapezoidal rule with higher order accuracy is proposed and corresponding error analysis is also obtained. Based on the proposed rule, a new collocation scheme is then constructed to solve certain finite-part integral equation, with the optimal error estimate being rigorously derived. Some numerical experiments are also performed to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12802
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 240–254
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Hadamard finite-part integral equation quadrature rule collocation method error analysis.