Atkinson, Kendall E.; Potra, Florian A. Projection and iterated projection methods for nonlinear integral equations. (English) Zbl 0655.65146 SIAM J. Numer. Anal. 24, 1352-1373 (1987). The authors study the numerical approximation of an isolated fixed point of a completely continuous mapping, acting in a Banach space, by the projection method and the iterated projection method. The abstract results obtained in Banach or Hilbert space setting is then detailed for Urysohn integral equations in L 2(\(\Omega)\) or \(L^{\infty}(\Omega)\), with \(\Omega\) a bounded compact subset in \({\mathbb{R}}^ m \)with nonempty interior, showing the superconvergence of the Galerkin method and the collocation method. Two numerical examples are also commented. Reviewer: S.Sburlan Cited in 1 ReviewCited in 83 Documents MSC: 65R20 Numerical methods for integral equations 65J15 Numerical solutions to equations with nonlinear operators 45G10 Other nonlinear integral equations 47J25 Iterative procedures involving nonlinear operators Keywords:isolated fixed point; completely continuous mapping; Banach space; iterated projection method; Hilbert space; Urysohn integral equations; superconvergence; Galerkin method; collocation method; numerical examples PDFBibTeX XMLCite \textit{K. E. Atkinson} and \textit{F. A. Potra}, SIAM J. Numer. Anal. 24, 1352--1373 (1987; Zbl 0655.65146) Full Text: DOI Link