Iterative Collocation Method for Solving a class of Weakly Singular Volterra Integral Equations.

Abstract

In this dissertation , we presented some basic concepts, definitions, and necessary theorems for integral and integro-differential equations and their Classified has been presented.Then,we have used an iterative ollocation method based on the Lagrange polynomials for solving a class of nonlinear weakly singular Volterra integral equations in the spline spaceS−1 m−1(I,ΠN). The main advantages of this method that, is easy to implement, has high order of convergence and the coefficients of approximate solution are determined by using iterative formulas without solving any system of algebraic equations. The numerical examples confirm that the method is convergent with a good accuracy.