On the Analytical and Numerical Study for Nonlinear Fredholm Integro-Differential Equations

Authors

Amira Abd-Elall Ibrahim, October High Institute for Engineering and Technology, Nasr-City, Cairo, EgyptFollow
Afaf A. S. Zaghrout, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptFollow
K. R. Raslan, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptFollow
Khalid K. Ali, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, we investigate the existence of a unique solution to nonlinear Fredholm integro-differential equation. The exact solution of the proposed equation using the direct calculation method is given. We combine the finite difference method with the composite Simpson method to find the numerical solution of the equation. The error estimate of our scheme is discussed in this article. Finally, to illustrate the accuracy of the proposed method, we give five numerical examples and compare the exact solution with the numerical solution.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140520

Recommended Citation

Abd-Elall Ibrahim, Amira; A. S. Zaghrout, Afaf; R. Raslan, K.; and K. Ali, Khalid (2020) "On the Analytical and Numerical Study for Nonlinear Fredholm Integro-Differential Equations," Applied Mathematics & Information Sciences: Vol. 14: Iss. 5, Article 20.
DOI: http://dx.doi.org/10.18576/amis/140520
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss5/20