The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data
Provides theoretical justification for a numerical method to stably solve a class of ill-posed integral equations, which is incremental for researchers in numerical analysis.
The paper analyzes the regularizing properties of the repeated midpoint rule for solving weakly singular Volterra integral equations of the first kind with perturbed data, proving inverse stability via Banach algebra techniques and presenting numerical results.
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 Hölder 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.