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Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

  • Y. H. YoussriEmail author
  • R. M. Hafez
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Abstract

This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

Mathematics Subject Classification

65R20 65M70 42C10 

Notes

Acknowledgements

We are indebted to the anonymous reviewers for their instructive comments. Thanks are due to Prof. N. Tatar for helping in a final draft proofreading.

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of Mathematics, Alwagjh University CollegeUniversity of TabukTabukSaudi Arabia
  3. 3.Department of Basic ScienceInstitute of Information Technology, Modern AcademyCairoEgypt

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