Numerical solution of some Volterra nonlinear integral equations by using spline iterative Collocation method.

Abstract

The main purpose of this thesis is to provide a direct, convergent and easy to implement numerical method to obtain the approximate solution for nonlinear delay Volterra integral equations. Algorithms based on iterative collocation method is developed for the numerical solution of these kinds of equations. We also provide a rigorous error analysis. A theoretical proof is given and we present some numerical results which illustrate the performance of the methods.