Iterated Galerkin versus Iterated Collocation for Integral Equations of the Second Kind |
| |
Authors: | GRAHAM IVAN G; JOE STEPHEN; SLOAN LAN H |
| |
Institution: |
School of Mathematics, University of Bath Claverton Down, Bath BA2 7AY
School of Mathematics, University of New South Wales Sydney, N.S.W. 2033, Australia
|
| |
Abstract: | We consider the numerical solution of one-dimensional Fredholmintegral equations of the second kind by the Galerkin and collocationmethods and their iterated variants, using spline bases. Inparticular, we state and prove new superconvergence resultsfor the iterated solutions, under general smoothness requirementson the kernel and solution. We find that the smoothness requirementsfor the iterated collocation method are more stringent thanthose for the iterated Galerkin method, and show by examplethat these more stringent smoothness conditions are in a certainsense necessary. In the light of these results the Galerkinand collocation schernes are compared. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|