ASYMPTOTIC ERROR EXPANSION OF A COLLOCATION-TYPE METHOD FOR HAMMERSTEIN EQUATIONS

In recent papers Kumar and Sloan have considered the numerical solutio n of the Hammerstein equation y(x) = f(x) + integral(a)(b) k(x, t)g(t, y(t)) dt, x is an element of [a, b] by a method that first applied th e standard collocation procedure to an equivalent equation for z(t) = g(t, y(t)) and then obtained an approximation to y by use of the equat ion y(x)=f(x) + integral(a)(b) k(x,t)z(t)dt, x is an element of [a, b] . In this paper, the asymptotic error expansion of this method is obta ined. We show that when piecewise polynomial of Pi(p-1) are used, the approximation solution admits an error expansion in even powers of the step-size h, beginning with a term h(2p). Thus, Richardson's extrapol ation can be performed on the solution and this will increase the accu racy of numerical solution greatly.