A Homotopy Based Method for Nonlinear Fredholm Integral Equations

Javed Ali*
Senior Lecturer, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Oman.
Periodicity:January - March'2018
DOI : https://doi.org/10.26634/jmat.7.1.14027


In this work, the author extends the application of the optimal homotopy asymptotic method to the solution of nonlinear Fredholm integral equations of the second kind. Several examples are solved to demonstrate the efficiency of the proposed method. Numerical results are compared with the exact solution.


Nonlinear Fredholm Integral Equation, Optimal Homotopy Asymptotic Method, Approximate Solutions.

How to Cite this Article?

Javed Ali. (2018). A Homotopy Based Method For Nonlinear Fredholm Integral Equations. i-manager’s Journal on Mathematics, 7(1), 13-17. https://doi.org/10.26634/jmat.7.1.14027


[1]. Abbasbandy, S. (2006). Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method. Applied Mathematics and Computation, 173(1), 493-500.
[2]. Abbasbandy, S., & Shivanian, E. (2011). A new analytical technique to solve Fredholm's integral equations. Numerical Algorithms, 56(1), 27-43.
[3]. Ali, J., Islam, S., Islam, S., & Zaman, G. (2010a). The solution of multipoint boundary value problems by the optimal homotopy asymptotic method. Computers & Mathematics with Applications, 59(6), 2000-2006.
[4]. Ali, J., Islam, S., Rahim, M. T., & Zaman, G. (2010b). The solution of special twelfth order boundary value problems by the optimal homotopy asymptotic method. World Applied Sciences Journal, 11(3), 371-378.
[5]. Ali, J., Islam, S., Shah, S., & Khan, H. (2011). The optimal homotopy asymptotic method for the solution of fifth and sixth order boundary value problems. World Applied Sciences Journal, 15(8), 1120-1126.
[6]. Ali, J., Islam, S., Khan, H., & Zaman, G. (2017). The solution of a parameterized sixth-order boundary value problem by the Optimal Homotopy Asymptotic Method. Proceedings of the Romanian Academy, Series A, 12(3), 167-172.
[7]. Almousa, M., & Ismail, A. (2013). Optimal homotopy asymptotic method for solving the linear Fredholm integral equations of the first kind. In Abstract and Applied Analysis, Article ID 278097, 1-6.
[8]. Ghorbani, A. (2009). Beyond Adomian polynomials: He polynomials. Chaos, Solitons & Fractals, 39(3), 1486-1492.
[9]. Ghorbani, A., & Saberi-Nadjafi, J. (2007). He's homotopy perturbation method for calculating Adomian polynomials. International Journal of Nonlinear Sciences and Numerical Simulation, 8(2), 229-232.
[10]. Hasan, M., & Mateen, A. (2017). Solving nonlinear integral equations by using Adomian decomposition method, Journal of Applied & Computational Mathematics, 6(2), 1-4.
[11]. Herisanu, N., Marinca, V., Dordea, T., & Madescu, G. (2008). A new analytical approach to nonlinear vibration of an electrical machine. Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, 9(3), 229-236.
[12]. Islam, J. A. S., Ali, I., & Khan, H. (2012). Application of optimal homotopy asymptotic method to higher order boundary value problems. In Abstract and Applied Analysis, Article ID 401217.
[13]. Jerri, A. A., (1985). Introduction to Integral Equations with Applications. Marcel Dekker Inc.
[14]. Li, H., & Huang, J. (2016). A novel approach to solve nonlinear Fredholm integral equations of the second kind. Springer Plus, 5(1), 154.
[15]. Marinca, V., & Herisanu, N. (2008). Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer. International Communications in Heat and Mass Transfer, 35(6), 710-715.
[16]. Ray, S. S., & Sahu, P. K. (2013). Numerical methods for solving Fredholm integral equations of second kind. In Abstract and Applied Analysis, Article ID 426916, 1-17.
[17]. Wazwaz, A. M. (2015). A First Course in Integral Equations. World Scientific Publishing Company.
[18]. Zemyan, S. M. (2012). The Classical Theory of Integral Equations: A Concise Treatment. Springer Science and Business Media.

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

If you have access to this article please login to view the article or kindly login to purchase the article
Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.