×

Projection and iterated projection methods for nonlinear integral equations. (English) Zbl 0655.65146

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

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
PDFBibTeX XMLCite
Full Text: DOI Link