Projection-type methods for nonlinear integral equations with non-smooth kernels

Abstract

In this paper, we explore two methods for estimating the solution
of Urysohn integral equations with a Green's function type kernel:
the Kantorovich approach and a projection-type method. Either the
orthogonal projection or an interpolatory projection onto the space
of piecewise polynomials of degre r is used as the approximating
operator. Compared to the projection-type solutions, it is shown that
if the right hand side of the operator equation is only continuous,
then the iterated Kantorovich solution converge more rapidly. However,
the projection-type method has lower computational costs. Several
numerical examples are provided to validate the theoretical estimates.