Series Solution for Single and System of Non-linear Volterra Integral Equations
Abstract
In this paper, Taylor expansion has been used for solving non-linear Volterra integral equations (VIEs) of the second kind. This method allows us to overcome the difficulty caused by integrals and non-linearity; also, it has more precise and rapidly convergent to the exact solution. Two examples are presented for illustrate the performance of this method.
Downloads
References
J. L. Hess. Review of integral-equation techniques for solving potential-flow problems with emphasis on the surface-source method. Computer Methods in Applied Mechanics and Engineering, vol. 5, no. 2, pp. 145-196, 1975.
S. A. Edalatpanah and E. Abdolmaleki. A new collocation method for systems of nonlinear fredholm integral equations. Applied Mathematics and Physics, vol. 2, no. 1, pp. 15-18, 2014.
H. Ibrahim, F. Attah, G. T. Gyegwe. On the solution of volterrafredholm and mixed volterra-fredholm integral equations using the new iterative method. Applied Mathematics, vol. 6, no. 1, pp. 1-5, 2016.
A. M. Wazwaz. Linear and Nonlinear Integral Equations. Berlin: Springer, 2011.
R. K. Saeed. Computational Methods for Solving System of Linear Volterra Integral and Integro-Differential Equations (Doctoral Dissertation, Ph. D. Thesis, University of Salahaddin/Erbil-Collage of Science), 2006.
P. J. Davis. Interpolation and Approximation. New York: Dover Publication, Inc., 1975.
K. E. Atkinson. An Introduction to Numerical Analysis. 2nd ed. Hoboken, New Jersey: John Wiley and Sons, 2008.
S. C. Chapra, R. P. Canale. Numerical Methods for Engineers. 4th ed. Boston: McGraw-Hill Higher Education, 2010.
E. W. Cheney, D. R. Kincaid. Numerical Mathematics and Computing. Monterey County: Cengage Learning, Brooks/Cole Publishing Company, 2012.
G. Hall, J. M. Watt. Modern Numerical Methods for Ordinary Differential Equations. Oxford: Oxford University Press, 1976.
C. T. Baker, G. F. Miller. Treatment of Integral Equations by Numerical Methods: Based on the Proceedings of a Symposium Held in Durham from 19-29 July, 1982, Organized under Auspices of the London Mathematical Society. London: Academic Press, 1982.
L. M. Delves, J. Walsh. Numerical Solution of Integral Equations. Oxford, England: Claredon Press Oxford, 1974.
O. A. Faour. Solving non-linear integral equations using (B2-Spline) function. Journal of University of Babylon for Pure and Applied Sciences, vol. 7, no. 3, pp. 372-377, 2002.
R. P. Kanwal, K. C. Liu. A Taylor expansion approach for solving integral equations. International Journal of Mathematical Education in Science and Technology, vol. 20, no. 3, pp. 411-414, 1989.
A. J. Jerry. Introduction to Integral Equations with Applications, a Series of Monographs and Textbooks. New York: Marcel Dekker, Inc., 1985.
A. M. Wazwaz. The modified decomposition method for analytic treatment of non-linear integral equations and systems of nonlinear integral equations. International Journal of Computer Mathematics, vol. 82, no. 9, pp. 1107-1115, 2005.
Copyright (c) 2020 Narmeen N. Nadir

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-ND 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).