Iterative Collocation Method for Second-Order Volterra Integro-Differential Equations

This paper presents a novel approach to solve nonlinear second-order Volterra integro-differential equations (VIDEs) using the Iterative Collocation Method. We focus on specific VIDEs with smooth functions, aiming to obtain numerical solutions without the need to solve algebraic equation systems. Our method, based on Lagrange polynomials within a spline space, offers direct implementation, high convergence order, and efficient determination of approximation solution coefficients. Through theoretical analysis and numerical experiments, we illustrate the efficacy and accuracy of our approach, contributing to the improvement of numerical techniques for solving nonlinear VIDEs.