Numerical analysis of a collocation method for functional integral equations

We study the numerical approximation of functional integral equations, a class of nonlinear Fredholm-type integral equations of the second kind, by the collocation method with piecewise continuous basis functions. The resulting nonlinear algebraic system is solved with the Picard iteration method. Starting from the analysis of the continuous problem in L∞([a,b]), we prove the convergence of numerical solution and, under an additional regularity assumption, provide an a priori error estimate. Numerical examples illustrate the predicted theoretical results.