Abstract:
In this research thin films of (ZnS) have been prepared as pure and doped by Aluminum (Al), Copper (Cu) and Nickel (Ni) with different ratio (i.e 2% , 5%), the films were prepared by chemical spray Pyrolysis from zinc chloride (ZnCl2) and thioriaa (CS(NH2)2) at substrate temperature (583K). The structural properties of thin films were studied by using reflective optical microscope and x-ray diffraction. Were appeared that the thin films have polycrystalline structure type (Zincblende) and the doping processes did show obvious effect on crystal structure of (ZnS) films doping with (Cu and Ni) where became near from amorphous structure, also calculated the lattice constant (a) and its values decreased after doping process. From studying of optical properties for range of wave length (300-900nm), the transmission were (75-85%), where doping process did show decreases in transmission of thin films because extinction increasing in radiation intensity after doping. Also calculated the optical constant such as absorption coefficient (), extinction coefficient (K) and energy gap (Eg) for direct electronic transitions where value equal to (3.42eV) before doping and between (3.38-3.02)eV after doping depending on material and concentration doping. Finally, the electrical properties for all films were studied through variation of resistively () with temperature for range (303-413)K and calculated the electrical conductivity () and activation energy (Ea). As a result of the doping process the conductivity was increased but the activation energy was decreased, from Seebeck effect investigations showed all films were of (n – type), and from the measurements of the activation energy of electro-thermal power (Es) that the its values was increased after doping and from it calculated the activation energy of mobility (E) where equal to different between (Ea) and (Es).

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).