Abstract

Abstract:
The main aim of this thesis is to study and modify some analytic and numerical methods to treat a system of linear second kind Volterra integral equations. For the analytic treatment two methods for solving single Volterra integral equation including Laplace transform and successive approximation method have been modified to be applicable to solve the system. Runge-Kutta methods including: Runge-Kutta second order, Runge-Kutta third order and Runge-Kutta of fourth order have been modified to give numerical solution to this system and study the convergent of the algorithms of Runge-Kutta methods. In addition, block methods which include: method of two, three and four blocks have been used to find numerical solution to this system. The package “NSSLSKVIE” is constructed to find the numerical solutions to system of linear Volterra integral equations using all the above methods. Finally, at the end of each method, algorithms and programs are developed and written in MATLAB (Version 6.5).