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Abstract
In this paper, we analyse the iterated collocation method for the nonlinear operator equation x = y+K(x) with K a smooth kernel. The paper expands the study begun by H. Kaneko and Y. Xu concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. Let x* denote an isolated fixed point of K. Let X
n
, n≥1, denote a sequence of finite-dimensional approximating subspaces, and let P
n
be a projection of X onto X
n
. The projection method for solving x = y+K(x) is given by x
n
= P
n
y+P
n
K(x
n
), and the iterated projection solution is defined as . We analyse the convergence of {x
n
} and {
} to x*, giving a general analysis that includes the collocation method. A detailed analysis is then given for a large class of Urysohn integral operators in one variable, showing the superconvergence of {
} to x*.