Theoretical and numerical results about some weakly singular Volterra-Fredholm equations

Abstract

In this paper existence, uniqueness results for the solution of some weakly singular linear Volterra and Volterra-Fredholm integral equations are given. For these equations, a numerical model is proposed and its convergence and rate of convergence are analyzed. Numerical results on some polynomial test functions are given.

Keywords

• weakly singular integral equations
• fixed points
• collocation method