Multiple grid methods for the solution of Fredholm integral equations of the second kind

Abstract

In this paper multiple grid methods are applied for the fast solution of the large nonsparse systems of equations that arise from the discretization of Fredholm integral equations of the second kind. Various multiple grid schemes, both with Nyström and with direct interpolation, are considered. For these iterative methods, the rates of convergence are derived using the collectively compact operator theory by Anselone and Atkinson. Estimates for the asymptotic computational complexity are given, which show that the multiple grid schemes result in O ( N 2 ) \mathcal {O}({N^2}) arithmetic operations.