A new strategy for the numerical solution of nonlinear Volterra integral equations with vanishing delays

Abstract

The aim of this paper is to develop a high-order algorithm for nonlinear Volterra integral equations with vanishing variable delays. The algorithm is a non-trivial extension of the single-step methods. This method is based on the variational form, so the algorithm is relatively simple. This scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. We prove the existence and uniqueness of the numerical solution, and derive error estimates of the algorithm. Numerical results show a good agreement with the theoretical analysis.