The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data
Numerical Analysis
2017-09-12 v1
Abstract
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind with perturbed right hand sides. The H\"older continuity of the solution and its derivative is carefully taken into account, and correction weights are considered to get rid of initial conditions. The proof of the inverse stability of the quadrature weights relies on Banach algebra techniques. Finally, numerical results are presented.
Keywords
Cite
@article{arxiv.1709.03142,
title = {The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data},
author = {Robert Plato},
journal= {arXiv preprint arXiv:1709.03142},
year = {2017}
}