A CELL-AVERAGING CHEBYSHEV SPECTRAL METHOD FOR NONLINEAR FREDHOLM-HAMMERSTEIN INTEGRAL-EQUATIONS

In this paper we present a cell-averaging Chebyshev spectral method fo r solving Fredholm-Hammersten integral equations of the form y(t)=f(t) +integral(-1)(1)k(t,s)g(s,y(s))ds, t epsilon[-1,1] The method is first applied to an equivalent integral equation of the form z(t)=g(t,y(t)) , where the function z is approximated by a Chebyshev polynomial, z(N) , of the first kind. We then seek a Chebyshev polynomial solution y(N) to y via y(N)(t)=f(t)+integral(-1)(1)k(t,x)z(N)(s)ds and establish th e uniform convergence of y(N) to y. Illustrative examples are included and comparison is made with the existing methods in the literature.