Orthonormal Bernstein polynomials for Volterra integral equations of the second kind

  • Authors

    • Jafar Biazar University of Guilan
    • Hamed Ebrahimi University of Guilan

    How to Cite

    Biazar, J., & Ebrahimi, H. (2020). Orthonormal Bernstein polynomials for Volterra integral equations of the second kind. International Journal of Applied Mathematical Research, 9(1), 9-20. https://doi.org/10.14419/ijamr.v9i1.29636

    Received date: July 14, 2019

    Accepted date: August 23, 2019

    Published date: March 25, 2020

    https://doi.org/10.14419/ijamr.v9i1.29636
  • Volterra‏ ‏Integral Equations, Linear Integral Equations, Orthonormal Bernstein Polynomials, Gram- Schmidt's Process, Moments (Galerkin- Ritz).

  • Abstract

    The purpose of this research is to provide an effective numerical method for solving linear Volterra integral equations of the second kind. The mathematical modeling of many phenomena in various branches of sciences lead into an integral equation. The proposed approach is based on the method of moments (Galerkin- Ritz) using orthonormal Bernstein polynomials. To solve a Volterra integral equation, the ap-proximation for a solution is considered as an expansion in terms of Bernstein orthonormal polynomials. Ultimately, the usefulness and extraordinary accuracy of the proposed approach will be verified by a few examples where the results are plotted in diagrams, Also the re-sults and relative errors are presented in some Tables.

     

     

  • References

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  • How to Cite

    Biazar, J., & Ebrahimi, H. (2020). Orthonormal Bernstein polynomials for Volterra integral equations of the second kind. International Journal of Applied Mathematical Research, 9(1), 9-20. https://doi.org/10.14419/ijamr.v9i1.29636

    Received date: July 14, 2019

    Accepted date: August 23, 2019

    Published date: March 25, 2020