An iterative scheme for numerical solution of Volterra integral equations using collocation method and Chebyshev polynomials

When we discretize nonlinear Volterra integral equations using some numerical, such as collocation methods, the arising algebraic systems are nonlinear. Applying quasilinear technique to the nonlinear Volterra integral equations gives raise to linear Volterra integral equations. The solutions of these equations yield a functional sequence quadratically convergent to the solution. Then, we use collocation method based on Chebyshev polynomials and a modified Clenshaw-Curtis quadrature and obtain a numerical solution. Error analysis has been performed, and the method has been applied on three numerical examples.