Modified Euler’s method with a graded mesh for a class of Volterra integral equations with weakly singular kernel

A modified Euler’s method applied on a graded mesh is considered for numerical solution of a class of Volterra integral equations with weakly singular kernel which depends on a parameter μ > 0. It is shown that the convergence rate of the considered method is higher than those of earlier ones for the case when μ ≤ 1. The convergence rate is also obtained in the case μ > 1. Using some numerical examples, we illustrate the theoretical results.