An Analytical Approximate Solution of Linear, System of Linear and Non Linear Volterra Integral Equations Using Variational Iteration Method

Abstract

In this paper we have solved Linear Volterra Integral Equations (LVIE), System of Linear Volterra Integral Equation (SLVIE) and non Linear Volterra Integral Equation (NLVIE) using variational Iteration Method (VIM). VIM is a powerful tool to solve the differential equations as well as integral equations. VIM gives consecutive approximations which converge rapidly to the exact solution in the given domain for the given initial condition, if it exists, without any transformation or any restrictive assumptions to non linear terms, which may change the physical behaviour of the problem, otherwise few approximations are enough only for numerical purposes. To exhibit the ability, accuracy and reliability of the method we have provided two problems of Linear Volterra Integral Equations, one problem of system of Linear Volterra Integral Equation and one problem of Non Linear Volterra Integral Equation. The study highlights the heaviness of the method.