Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials

Orthogonal Chebyshev polynomials are developed to approximate the solutions of linear and nonlinear Volterra integral equations. Properties of these polynomials and some operational matrices are first presented. These properties are then used to reduce the integral equations to a system of linear or nonlinear algebraic equations. Numerical examples illustrate the pertinent features of the method.