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Full-Text Articles in Physical Sciences and Mathematics
Superconvergence Of The Iterated Collocation Methods For Hammerstein Equations, Hideaki Kaneko, Richard D. Noren, Peter A. Padilla
Superconvergence Of The Iterated Collocation Methods For Hammerstein Equations, Hideaki Kaneko, Richard D. Noren, Peter A. Padilla
Mathematics & Statistics Faculty Publications
In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].
Superconvergence Of The Iterated Galerkin Methods For Hammerstein Equations, Hideaki Kaneko, Yuesheng Xu
Superconvergence Of The Iterated Galerkin Methods For Hammerstein Equations, Hideaki Kaneko, Yuesheng Xu
Mathematics & Statistics Faculty Publications
In this paper, the well-known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numerical examples are presented to illustrate the superconvergence of the iterated Galerkin approximation for Hammerstein equations with weakly singular kernels. © 1996, Society for Industrial and Applied Mathematics
Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu
Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu
Mathematics & Statistics Faculty Publications
In the recent paper [7], it was shown that the solutions of weakly singular Hammerstein equations satisfy certain regularity properties. Using this result, the optimal convergence rate of a standard piecewise polynomial collocation method and that of the recently proposed collocationtype method of Kumar and Sloan [10] are obtained. Superconvergence of both of these methods are also presented. In the final section, we discuss briefly a standard productintegration method for weakly singular Hammerstein equations and indicate its superconvergence property. © 1992 Rocky Mountain Mathematics Consortium.