The numerical solution of Hammerstein equations by a method based on polynomial collocation

Abstract

In recent papers we have considered the numerical solution of the Hammerstein equation by a method which first applies the standard collocation procedure to an equivalent equation for z(t):= g(t, y(t)), and then obtains an approximation to y by use of the equation In this paper we approximate z by a polynomial z_n of degree ≤ n − 1, with coefficients determined by collocation at the zeros of the nth degree Chebyshev polynomial of the first kind. We then define the approximation to y to be and establish that, under suitable conditions, , uniformly in t.