Taylor series method for solving linear fredholm integral equation of second kind using matlab

Abstract EN

This paper presents a new method to find the approximation solution for linear feedhole integral equation : y (x) = ƒ (x) + λ ∫_a^b▒k (x, t) y (t) by using Taylor series expansion to approximate the kernel k (x, t) as a summation of multiplication functions ƒn (x) by gn (t) i.

e.

k (x, t) = ∑_(n=1)^N▒〖fn (x)g n (t)〗Then use the degenerate kernel idea to solve the freehold integral equation .In this paper we solve the above integral equation with a = 0 and b = 1, λ is a real number, f (x) and k (x, t) are real continues functions.

We have deduced a MATLAB program to solve the above equation ; we have used MATLAB (R2008a) to perform this program.

The presented method has high accurate when compare its results with the other analytical methods results.