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Math. Comput. Appl. 2013, 18(1), 19-29; doi:10.3390/mca18010019

Approximate Solutions of Linear Fredholm Integral Equations System with Variable Coefficients

Department of Mathematics Celal Bayar University, 45047, Muradiye, Manisa, Turkey
Published: 1 April 2013
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Abstract

In this paper, a new approximate method has been presented to solve the linear Fredholm integral equations system (FIEs). The technique 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. Also, this method gives the analytic solution when the exact solutions are polynomials. So as to Show this capability and robustness, some systems of FIEs are solved by the presented method in order to obtain their approximate solutions.
Keywords: Taylor polynomials and series; system of integral equations; Fredholm systems Taylor polynomials and series; system of integral equations; Fredholm systems
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Yalçınbaş, S. Approximate Solutions of Linear Fredholm Integral Equations System with Variable Coefficients. Math. Comput. Appl. 2013, 18, 19-29.

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