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
Received 03 December 2019; Accepted 24 February 2020; Issue published 28 May 2020
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
Cite This Article
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.