Solution of nonlinear VolterraHammerstein integral equations using alternative Legendre collocation method

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear VolterraHammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.