Numerical approximations of Fredholm integral equations with Abel kernel using Legendre and Chebychev polynomials
Abstract
In this study, Legendre and Chebychev collocation method are presented to solve numerically the Fredholm Integral Equations with Abel kernel. This method is based on replacement of the unknown function by truncated series of well known Legendre and Chebychev expansion of functions. This lead to a system of algebraic equations with Legendre and Chebychev coefficients. Thus, by solving the matrix equation, Legendre and Chebychev coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed technique.
Copyright © 2013 Chokri Chniti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
C. Chniti, Numerical approximations of Fredholm integral equations with Abel kernel using Legendre and Chebychev polynomials, J. Math. Comput. Sci. 3 (2013), 655–667.
BibTeX
@article{Chniti2013,
author = {Chniti, Chokri},
title = {Numerical approximations of Fredholm integral equations with Abel kernel using Legendre and Chebychev polynomials},
journal = {J. Math. Comput. Sci.},
volume = {3},
year = {2013},
pages = {655--667},
doi = {}
}