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Volume 16, Issue 2
A New Collocation Method for Solving Certain Hadamard Finite-Part Integral Equation

Hui Feng, Yan Gao, Lili Ju & Xiaoping Zhang

Int. J. Numer. Anal. Mod., 16 (2019), pp. 240-254.

Published online: 2018-10

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  • 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.

  • Keywords

Hadamard finite-part integral equation, quadrature rule, collocation method, error analysis.

  • AMS Subject Headings

65R20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hfeng.math@whu.edu.cn (Hui Feng)

sabrina8128@163.com (Yan Gao)

ju@math.sc.edu (Lili Ju)

xpzhang.math@whu.edu.cn (Xiaoping Zhang)

  • BibTex
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  • TXT
@Article{IJNAM-16-240, author = {Feng , HuiGao , YanJu , Lili and Zhang , Xiaoping}, title = {A New Collocation Method for Solving Certain Hadamard Finite-Part Integral Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12802.html} }
TY - JOUR T1 - A New Collocation Method for Solving Certain Hadamard Finite-Part Integral Equation AU - Feng , Hui AU - Gao , Yan AU - Ju , Lili AU - Zhang , Xiaoping JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 240 EP - 254 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12802.html KW - Hadamard finite-part integral equation, quadrature rule, collocation method, error analysis. AB -

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.

Feng , HuiGao , YanJu , Lili and Zhang , Xiaoping. (2018). A New Collocation Method for Solving Certain Hadamard Finite-Part Integral Equation. International Journal of Numerical Analysis and Modeling. 16 (2). 240-254. doi:
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