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Theoretical analysis of Sinc-Nyström methods for Volterra integral equations


Authors: Tomoaki Okayama, Takayasu Matsuo and Masaaki Sugihara
Journal: Math. Comp. 84 (2015), 1189-1215
MSC (2010): Primary 65R20; Secondary 45D05
DOI: https://doi.org/10.1090/S0025-5718-2014-02929-3
Published electronically: December 30, 2014
MathSciNet review: 3315505
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Abstract: In this paper, we present three theoretical results on Sinc-Nyström methods for Volterra integral equations of the first and second kind, which were proposed by Muhammad et al. Their methods involve the following issues: 1) it is difficult to determine the tuning parameter unless the solution is given, and 2) convergence has not been proved in a precise sense. In a mathematically rigorous manner, we present an implementable way to estimate the tuning parameter and a rigorous proof of the convergence with its rate explicitly revealed. Furthermore, we show that the resulting system is well conditioned. Numerical examples that support the theoretical results are also presented.


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Additional Information

Tomoaki Okayama
Affiliation: Graduate School of Economics, Hitotsubashi University, 2-1, Naka, Kunitachi, Tokyo, 186-8601, Japan
Email: tokayama@econ.hit-u.ac.jp

Takayasu Matsuo
Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo, 113-8656, Japan
Email: matsuo@mist.i.u-tokyo.ac.jp

Masaaki Sugihara
Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo, 113-8656, Japan
Email: m_sugihara@mist.i.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0025-5718-2014-02929-3
Received by editor(s): March 26, 2013
Published electronically: December 30, 2014
Additional Notes: The first author was supported by JSPS Grants-in-Aid for Scientific Research.
Article copyright: © Copyright 2014 American Mathematical Society

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