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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the collocation methods for singular integral equations with Hilbert kernel
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by Jinyuan Du PDF
Math. Comp. 78 (2009), 891-928 Request permission

Abstract:

In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods of numerical solutions of singular integral equations with Hilbert kernel is given. Under the framework, it is very simple and obvious to obtain the coincidence theorem of collocation methods, then the existence and convergence for constructing approximate solutions are also given based on the coincidence theorem.
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Additional Information
  • Jinyuan Du
  • Affiliation: Department of Mathematics, Wuhan University, Wuhan 430072, People’s Republic of China
  • Email: jydu@whu.edu.cn
  • Received by editor(s): June 20, 2007
  • Received by editor(s) in revised form: May 11, 2008
  • Published electronically: December 10, 2008
  • Additional Notes: This project was supported by NNSF of China (#10471107) and RFDP of Higher Eduction of China (#20060486001).
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 891-928
  • MSC (2000): Primary 65E05, 65J10, 41A55, 42A10
  • DOI: https://doi.org/10.1090/S0025-5718-08-02182-0
  • MathSciNet review: 2476564