THE ROLES OF A WEAK SINGULARITY AND THE GRID UNIFORMITY IN RELATIVE ERROR BOUNDS

Abstract

We develop a relative error bound specifying the role of the singularity and the one of the grid uniformity in the case of projection type approximations for the solution of a Fredholm integral equation of the second kind with a weakly singular kernel of convolution type. Numerical experiments with equations having solutions of different nature, namely continuous, integrable bounded discontinuous and integrable unbounded, complete this work. These experiments give an idea on how realistic the theoretical relative error estimates are, depending on the nature of the solution.

Acknowledgments