Applied Mathematics and Physics
ISSN (Print): 2333-4878 ISSN (Online): 2333-4886 Website: http://www.sciepub.com/journal/amp Editor-in-chief: Vishwa Nath Maurya
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Applied Mathematics and Physics. 2014, 2(2), 40-48
DOI: 10.12691/amp-2-2-3
Open AccessArticle

A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations

Salih Yalçınbaş1, and Kübra Erdem1

1Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, Manisa, Turkey

Pub. Date: February 28, 2014

Cite this paper:
Salih Yalçınbaş and Kübra Erdem. A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations. Applied Mathematics and Physics. 2014; 2(2):40-48. doi: 10.12691/amp-2-2-3

Abstract

In this paper, we present a new approximate method for solving systems of nonlinear Fredholm integral equation. This method is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Numerical results and comparisons with the exact solution are included to demostrate the validity and applicability of the technique.

Keywords:
nonlinear Fredholm systems Taylor polynomials and series

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