Solving nonlinear Volterra integro-differential equation by using Legendre polynomial approximations

‎In this paper‎, ‎we construct a new iterative method for solving nonlinear Volterra Integral Equation of second kind‎, ‎by approximating the Legendre polynomial basis‎. ‎Error analysis is worked using Banach fixed point theorem‎. ‎We compute the approximate solution without using numerical method‎. ‎Finally‎, ‎some examples are given to compare the results with some of the existing methods‎.