Discrete Galerkin Methods for Fredholm Integral Equations of the Second Kind

The discrete Galerkin and discrete iterated Galerkin methodsarise when the integrals required in the Galerkin and iteratedGalerkin methods are calculated using numerical integration.In this paper, prolongation and restriction operators are usedto give an error analysis for these two discrete Galerkin methods.From this analysis, we can then give conditions on the quadratureerrors, under which the two discrete Galerkin solutions havethe same order of convergence as their exact counterparts.