A numerical treatment to the solution of certain first kind Fredholm integral equations

This paper presents results obtained by an implementation of the kernel basis functions method to the solution of a special Fredholm integral equation of the first kind. The approximate solution is expressed in the linear form u_k(t)=∑w_jK(s_j, t), j=1, 2,..., k, where the unknown parameters w_j and s_j are determined by solving two linear overdetermined systems and a polynomial equation of the k-th order. Test examples are used to show that the numerical solution is comparable to the exact one.