Weakly Singular Discrete Gronwall Inequalities

Abstract

Abstract Generalizations of the classical Gronwall inequality when the kernel of the associated integral equation is weakly singular are presented. The continuous and discrete versions are both given; the former is included since it suggests the latter by analogy. This work is motivated by convergence studies of discretization methods for Volterra integral and integro‐differential equations. The results are all given in a form designed to be of most use to numerical analysts.