## Table of Content Open Access

ARTICLE

# Bell Polynomial Approach for the Solutions of Fredholm Integro-Differential Equations with Variable Coefficients

Gökçe Yıldız1, Gültekin Tınaztepe2, *, Mehmet Sezer1

1 Department of Mathematics, Faculty of Science, Manisa Celal Bayar University, Manisa, Turkey.
2 Vocational School of Technical Sciences, Akdeniz University, Antalya, Turkey.

* Corresponding Author: Gültekin Tınaztepe. Email: .

(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(3), 973-993. https://doi.org/10.32604/cmes.2020.09329

## Abstract

In this article, we approximate the solution of high order linear Fredholm integro-differential equations with a variable coefficient under the initial-boundary conditions by Bell polynomials. Using collocation points and treating the solution as a linear combination of Bell polynomials, the problem is reduced to linear system of equations whose unknown variables are Bell coefficients. The solution to this algebraic system determines the approximate solution. Error estimation of approximate solution is done. Some examples are provided to illustrate the performance of the method. The numerical results are compared with the collocation method based on Legendre polynomials and the other two methods based on Taylor polynomials. It is observed that the method is better than Legendre collocation method and as accurate as the methods involving Taylor polynomials.

## Keywords

Yıldız, G., Tınaztepe, G., Sezer, M. (2020). Bell Polynomial Approach for the Solutions of Fredholm Integro-Differential Equations with Variable Coefficients. CMES-Computer Modeling in Engineering & Sciences, 123(3), 973–993. This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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