Projection and iterated projection methods for nonliear integral equations
SIAM Journal on Numerical Analysis
A discrete collocation-type method for Hammerstein equations
SIAM Journal on Numerical Analysis
Extrapolation of a discrete collocation-type method of Hammerstein equations
Journal of Computational and Applied Mathematics
Superconvergence of the iterated Galerkin methods for Hammerstein equations
SIAM Journal on Numerical Analysis
Superconvergence of the iterated collocation methods for Hammerstein equations
Journal of Computational and Applied Mathematics
Collocation methods for solving multivariable integral equations of the second kind
Journal of Computational and Applied Mathematics
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In a recent paper, we introduced new methods called superconvergent Nystrom and degenerate kernel methods for approximating the solution of Fredholm integral equations of the second kind with a smooth kernel. In this paper, these methods are applied to numerically solve the Hammerstein equations. By using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree @?r-1, we prove that, as for Fredholm integral equations, the proposed methods exhibit convergence orders 3r and 4r for the iterated version. Several numerical examples are given to demonstrate the effectiveness of the current methods.