Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Authors

  • E. M. Abo-Eldahab Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt
  • A. S. Mohamed Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt https://orcid.org/0000-0001-9517-0296
  • S. M. Ali Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt

DOI:

https://doi.org/10.37256/cm.3320221489

Keywords:

Volterra integral equation, Fredholm integral equation, generalized Fibonacci polynomials, collocation method

Abstract

In this research article, we build and implement an efficient spectral algorithm for handling linear/nonlinear mixed Volterra-Fredholm integro-differential equations. First, we expand the exact solution as a truncated series of the generalized Fibonacci polynomials, and then we discretize the equation via Simpson's quadrature formula. Finally, we collocate the resulted residual at the roots of the shifted first-kind Chebyshev polynomials. Also, the rate of convergence is studied and the truncation error estimate is reported. Some numerical examples are exhibited to prove the applicability and accuracy of the algorithm.

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Published

2022-07-14

How to Cite

1.
Abo-Eldahab EM, Mohamed AS, Ali SM. Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials. Contemporary Mathematics [Internet]. 2022 Jul. 14 [cited 2022 Aug. 16];3(3):308-25. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1489